Introduction

In 2009, boardgamegeek user Kerning posted an interview he conducted with game designer Uwe Rosenberg, which has been translated from German. In response to a question about his preferences, Rosenberg responded:

My personal tendency is toward the most elaborate strategy games in which one cannot attack directly without provocation. If I think extensively about my game moves, then I don’t like it when others simply break my moves so that all thinking becomes redundant. Therefore I am pleased to be quoted for the observation that strategy and war are not part of games with three and more persons. A two-person game behaves quite differently. Here you have only one opponent and you prepare yourself so that every aggression that the opponent initiates will be met with one. This is calculable.

Here, Rosenberg succinctly explains why games with different numbers of players should address player interaction differently. In this article I define player interaction and discuss what properties of games arise from player interaction depending on the number of players. Ultimately, I hope to address an ongoing discussion among gamers about the value and role of player interaction, and the legitimacy of game designs which limit player interaction.

Multiplayer Games

Most modern board games accommodate more than two players. Furthermore, most of these “multiplayer games,” here meaning games with more than two players, are “free-for-alls,” meaning that each player is trying to win for him or herself as opposed to being on a team. At the time of writing this article, 65% of the top 100 board games on boardgamegeek.com are multiplayer free-for-alls and 20% are strictly 1v1 games. Certainly there are other categories of games: there are one-player games and team games with one team (cooperative games), two teams (Descent, Captain Sonar, Fury of Dracula), or more. In this post, however, I will focus on multiplayer free-for-alls compared with 1v1 games.

The abundance of modern multiplayer free-for-all board games stands in contrast to other types of games, most obviously traditional competitive board games like Chess and Go, which are strictly for two players. Furthermore, most competitive sports are either two-player games (tennis, martial arts), two-team games (football, baseball) or highly multiplayer (track-and-field competitions, swimming, gymnastics). It is important to note that these highly multiplayer sports often more like simultaneous 1-player games where players compete to get the highest score – there is significantly less player interaction in these games than in games like tennis or football.

Similarly, the most competitive forms of most competitive video games are usually either for two players or two teams. Starcraft and Starcraft II tournaments are generally played in 1v1 mode and occasionally 2v2 mode, while free-for-all mode is relegated to unranked non-competitive play. Most major MOBA games (Dota and Dota 2, League of Legends, Heroes of the Storm) are also 2-team games, as well as World of Warcraft Arena and Overwatch. Some games which were designed as multi-player free-for-alls such as Super Smash Brothers are mostly played as 1v1 games in competitive settings. There are some highly competitive video games which are most commonly played as multiplayer free-for-alls such as Halo and Call of Duty, although they are less common in competitive settings. Finally, there also exist highly multiplayer simultaneous one-player game competitions in video games, as in the case of competing for high scores at arcade games or Guitar Hero, or in speedrun competitions.

But board games tend to accommodate at least three players, perhaps because of their traditional role as social activities for families and small groups of friends. If board games were like sports, then, we would expect them to either take the form of 2-team games or true multiplayer solitaire, where players cannot interact with each other. However, gamers will often criticize certain board games for being like multiplayer solitaire, in that they have too little player interaction. We want to play with our friends, not just alongside them, and thus the amount of player interaction you would find in a swimming, track-and-field, or video game speedrun competition is considered too little.

Why, then, are there so many games which have such limited player interaction? Why limit player interaction at all? For instance, in most modern economic games, why are players not allowed to freely trade resources with each other? Why can’t we build armies in Terra Mystica? In order to answer these questions, I will attempt to talk about player interaction in general and what emergent properties it can introduce into a game. Finally, I will attempt to explain how some properties of modern Eurogames can be seen as a solution to the problem of player interaction in the unusual setting of multiplayer games.

What is Player Interaction?

Player interaction is widely discussed, as in “how much player interaction is in this game?” or “what is your favorite form of player interaction?” Usually there is no confusion, because player interaction seems to be a straightforward idea, but in writing this article I have found the need to take a step back and try to define player interaction precisely, as follows:

A game is a series of decisions by players. Let us say Decision A is facilitated by Decision B if the options which constitute Decision A depend on the outcome of Decision B. For instance, if another player destroys some of my armies, I no longer have the option to move those armies into Kamchatka. Decision A is informed by Decision B if the utility of the various possible choices in Decision A depend on Decision B. For instance, if another player adds more of his armies to Kamchatka, it may be less appealing for me to invade.

The degree of reactivity of a player’s decision to his opponent’s decision is the degree to which his decision is informed or facilitated by his opponent’s. Then interaction is simply what occurs when players each make decisions which are reactive to the decisions of each other. The degree of interactivity in a game is some summary of the amount of reactivity in the decisions which take place throughout the course of the game.

Three Push-Your-Luck Games

For illustrative purposes, I will describe a series of games, each with more player interaction than the last.

Game 1 is a prototypical push-your-luck game wherein each player repeatedly rolls a six-sided die. After each roll, a player may choose to roll again or stop. If a player stops, her final score is the sum of all of her die rolls. However, if at any point a player rolls a 6, that player “busts” and her final score is 0. Moreover, the players of Game 1 play in separate rooms, so that they cannot communicate in any way until the next day when they compare their final scores. The player with the highest score wins the game.

This game seems to have very little player interaction, but in fact there is some. The reason is that in strategizing about Game 1, it is important to consider both the number of players playing the game and the decisions they might make. If there are n players in the game, the Nash Equilibrium strategy is to make decisions such that the distribution of your outcomes has a maximal (n-1)/n quantile. Or, if you happen to know a priori that your friends are all brash risk-takers that are likely never to stop, you might exploit their likely strategies by rolling conservatively. Although one does not observe the realizations of the decisions of one’s opponents, one reacts to a model of their decisions.

Game 2 is the same game except here all of the players play in a turn-based fashion around a table. Now, a player can use information about all other players’ current scores every time he decides whether to stop or continue. The strategic considerations in Game 2 are more extensive, because in a push your luck game, it is relevant to observe the outcomes of the decisions of one’s opponents. If a player can observe that one or several of his opponents have been eliminated, he can make more conservative decisions. If a player knows that at least one of his opponents has a higher score than he does, he should clearly not stop rolling even if it would be sensible to stop under other circumstances. Other players should then react to the realization of these decisions, and so on. Thus arises a greater degree of player interaction, even in a game wherein players cannot directly affect the score or assets of any other player.

Game 3 introduces an element of “take-that,” in that players each start the game with a token. A player can spend his token to either reduce an opponent’s die roll by 3 before it resolves, or they can spend the token at the beginning of another player’s turn to eliminate that player’s option to stop that turn, thus forcing them to roll the die even if they didn’t want to. Here, not just the quality of the decisions, but the available decisions themselves may depend on the outcome of the decisions of other players.

Targeted Player Interaction

The “take-that” aspect of Game 3 is related to the concept of targeted player interaction. An interactive decision is targeted if it informs or facilitates the decisions of the other players in the game differently. In Game 3, if a player decides to use a token to remove his opponent’s option to stop rolling, he has facilitated his opponent’s new decision (which is now in fact a non-decision). If a player decides to use a token to reduce an opponent’s score by 3, he can inform the future decisions of that opponent, for instance if that opponent is now behind and thus has new incentives to continue rolling. In these situations, because the player does not facilitate or inform the decisions of his opponents equitably, he has engaged in targeted player interaction.



A decision which increases the utility of the choices of one player while leaving the other players’ decisions unchanged is targeted, as well as a decision to destroy the assets of some subset of the other players. Clearly, targeted player interaction is not a consideration in two-player games, since there is only one opponent. In most modern multiplayer board games, most decisions will be targeted to some extent. For instance, the mere act of taking five doubloons from the bank in a game will be a slight aggression to the player who stood to gain from having a comparative advantage in doubloons.

Discussion

These definitions of interaction and targeting can help us understand why a foot race is usually considered less interactive than a game of Yahtzee, which is less interactive than a war game. Player interaction occurs naturally in any game with competition, indeterminacy, and meaningful decisions (the three ingredients of Game 1). It is also worth noting that the amount of player interaction in a game is, as most characteristics of games, partially agential (meaning player-dependent). In some games which have the potential to be highly interactive, a group of particularly dim-witted players could completely ignore the role of the other players (as far as the rules allow), and in doing so end up playing a non-interactive game. When we think of the amount of interaction in a game, we have to also consider the players. I will discuss this further in the next section.

Player interaction can be desirable trait in games for social reasons, and also because it can generate interesting gameplay by forcing players to strategize in a way that is sensitive to the strategy of other players. This type of recursive reasoning is at the heart of game theory, and distinguishes the analysis of games from other types of optimization problems. However, I will argue, extensive targeted player interaction can have undesirable effects on the nature of a game. By examining the effects of targeted player interaction in two “contexts,” that of rational opponents and that of human opponents, we may be able to better explain how modern board games use certain rules and mechanism in order to address these emergent phenomena.

Two Contexts for Studying Games

In a game theoretically perfect world, a player could rely upon his opponents to act optimally. Therefore, their actions would be predictable to the extent that they would adopt an optimal strategy but may still be indeterminate to the extent that an optimal strategy for that particular game may involve some random choices (as in Rock, Paper, Scissors). Game theoretically optimal decisions are made by maximizing one’s chance of winning the game assuming that one’s opponent is also acting optimally.

Optimal strategies are rarely accessible in modern board games because they are designed to be outside the realm of solvability. Players will deviate from optimality either predictably or unpredictably. When a player’s strategy is not at equilibrium, that player can be exploited by opponents. Exploitative decisions can only exist where there are suboptimal players, because strategies at game theoretical equilibrium can, by definition, not be exploited.

Real-life players may play suboptimally due to their limitations in reasoning as humans as well as considerations which are external to the game itself. One common “metagame” consideration is that real-life players often have goals which do not align with the the victory condition of the game. A player may have a personal vendetta against another player or, conversely, external motivation to cooperate (with a spouse, perhaps). Players may cooperate at times when it is suboptimal to do so in order to gain the trust of other players in future games. Or, players may be attracted to the aesthetic aspects of certain decisions and thus prioritize them over maximizing their chance of winning. (The appeal of collecting a lot of animeeples in Agricola has led many players astray).

On the other hand, players may be earnestly attempting to maximize their probability of winning the game, but still fail to act optimally. These sub-optimal decisions cannot be fully predicted in the way that an opponent’s optimal decision might be deduced. However, players may have observable “play styles,” so they may act in predictable ways when faced with non-obvious decisions. An experienced player may be well aware of common pitfalls that plague newer players, and thus may be able to exploit them. Overall, while suboptimal decisions are not entirely arbitrary, they cannot be analyzed solely using knowledge of the game itself. To make predictions about what another player would do, we would have to use psychology, behavioral science, and maybe some information about what they ate for breakfast.

Therefore, I believe when we are analyzing a particular element of modern board games, we should ask ourselves two separate questions:

“How does this element affect the properties of the game and the nature and qualities of decisions which are optimal in the hypothetical setting of optimal opponents?” “How does this element affect the properties of the game and the nature and quality of decisions in the realistic setting of potentially exploitative, suboptimal players?”

In this post, I use this two-question framework to attempt to address player interaction in multiplayer games.

Multiplayer Interaction in Context A: Rational Opponents

Incentive Structures

In a two-player game, if the probability that Player 1 wins is p 1 and the probability that player 2 wins is p 2 , then there is a one-to-one relationship p 1 = 1-p 2 . The best choice for player 1 is always the choice that increases his odds the most. Therefore, in a two player game, increasing one’s standing is equivalent to decreasing the standing of one’s opponent. This fact encourages destructive player interaction in two player games such as combat and blocking. In Chess, for instance, a player may choose to trade pieces with his opponent, thus decreasing both players’ material value significantly but equally, in order to marginally increase the utility of his position. Meanwhile, it may be possible to make cooperative decisions in a two-player game, but this is only an attractive option for a player if he stands to gain more value from the cooperation than his opponent.

Things get a bit more complicated when we consider player interaction in multiplayer games. Now there is not just one ratio of odds to consider but several pairwise ratios. (In a 4 player game, for instance, there are 6 pairwise odds ratios between players). Unlike in a two player game, here it is possible for a player to make a decision which decreases her own standing and one or more of her opponents’ standings. There are two major strategic implications. First of all, sacrificing assets to decrease the assets of another player can now be especially counterproductive because in doing so a player decreases her pairwise odds ratio with uninvolved parties. Second of all, cooperating with other players can be much more attractive; even if a cooperative decision benefits a player’s opponent more than a player himself, it may still be optimal. This is because although a player may decrease one of his pairwise odds ratios through cooperation, he increases all of his other pairwise odds ratios with the uninvolved parties.

These are consequences of making a game “multiplayer” which are not necessarily a problem, although they do explain why naively porting a game of cutthroat player interaction from two players to multiple players doesn’t necessarily work. For instance, making chess into a four-player free-for-all with a player on each side of the square board would drastically change the strategic nature of the game. Now, trading pieces with an opponent would be a death sentence, because the players who didn’t lose any pieces would have an advantage. Players would then have incentive to “turtle up” on their own side of the board without ever advancing towards the center. This concept also explains why a game like Sheriff of Nottingham works with multiple players but wouldn’t work with only two. A corrupt sheriff has incentive to accept bribes from merchants even if the bribes are worth less than the merchant’s gains in contraband. If the sheriff takes such bribes from every player, he likely profits the most even though he gets the “worse end” of every individual deal.

Therefore, multiplayer games need to have different rules and incentive structures in order to facilitate player interaction. In order to facilitate destructive player interaction, multiplayer games may reward players for sacrificing their own assets to harm other players beyond simply increasing the difference in standing between those two players. Many modern board games reward players with victory points for engaging in combat (Eclipse, Scythe). In addition, multiplayer games may need to limit the utility of cooperative interaction, or disallow cooperative interaction entirely. For instance, in Settlers of Catan, the appeal of trading is limited by the possibility of losing one’s cards by the robber or a roll of 7 before one has a chance to spend the new cards. In most modern economic games like Agricola, trading resources with other players is entirely prohibited except perhaps through certain tightly controlled mechanisms. In Through the Ages, players can make minor cooperative “pacts,” but there are relatively few opportunities to do so and these pacts cost precious actions to put into play.

Damping

In the book Characteristics of Games, which I frequently mention on this blog, the authors often use a game called the “token taking game” as an example to illustrate certain effects of targeted player interaction. The most basic version of the game is played as follows:

Each player starts with an equal number of tokens. On your turn, you choose another player and discard one of his tokens. Once a player has no tokens, he is eliminated from the game. The last player standing wins.

This game is quite simple, and has an obvious equilibrium strategy, which is to always take a token from one of the players with the most tokens. Because the game is solved, assuming the players are rational game-theoretic agents, the winner is determined by turn order and other arbitrary factors. The game is essentially a king making game; in the last rounds, each player will need to decide whom to eliminate, and the decision is arbitrary because it does not affect each player’s own chance of winning. Furthermore, early game decisions, if made incorrectly, are completely irrelevant because these imbalances in assets should be corrected by other players later in the game.

A modified version of the token game is as follows:

Each player starts with an equal number of tokens. On your turn, you choose another player and play a game of Chess against that player. If you win, discard two of that player’s tokens. If you lose, discard one of that player’s tokens. The last player standing wins.

This modified version of the token taking game contains the entire game of Chess, and therefore has a very high skill ceiling. It is not solved, because chess has not been solved. Departing from the setting of optimal game-theoretic agents for a moment, imagine a group of players playing the modified token taking game who have disparate levels of skill at Chess, and thus disparate levels of skill at the modified token taking game. The result of the targeted, interactive nature of the token taking game is that the effect of skill on the outcome of the game will be reduced. Now the best strategy is to target the players who are better at Chess more frequently than one should target the players who aren’t as good at Chess. Having more tokens than other players early on in the game does little but make oneself a more attractive target. Depending on the number of players and the number of starting tokens, as long as every player is making reasonable decisions about whom to target based on their level of ability at Chess and the number of tokens that player has, then the winner of the game will be very close to uniformly random. The effect of skill on the outcome of the game will be entirely washed out by the level of player interaction in the game.

The example of the token-taking game informs our analysis of games in general. If a player has the potential to act upon other players, he has incentive to destructively interfere with the player who is in the lead. When it is to a player’s advantage to act cooperatively, he prefers to cooperate with opponents who are behind. Therefore, throughout the course of a game with targeted player interaction, the advantage of building one’s assets is lessened due to the fact that it will discourage others to cooperate with that person. Lagging behind other players is rewarded as one avoids becoming the target of destructive interaction. This force which constrains players’ odds and prevents their comparative odds from diverging is called damping.

Of course, damping differences in standing between players can be a good thing. Many games are designed in such a way that early game decisions have repercussions which are amplified throughout the game. Early game investments may yield exponential returns as the game progresses, which means that players who made better decisions (or got lucky) early on can wind up with disproportionately greater assets than their opponents. In order to keep things tightly competitive, games may exert damping forces in order to shrink the differences in standings between players. These mechanisms are often called “rubber-band mechanisms.” A notable example of a game which shrinks differences in standing automatically is Power Grid, wherein the players who are performing best by certain metrics (cities built, value of power plants) lose turn order initiative, facing higher prices and fewer options when buying power plants.

For lack of automatic, non-agential rubber-banding mechanisms, many games include targeted player interaction as a way of preventing run-away leaders and helping stragglers. For instance, in Settlers of Catan, players can refuse to trade with the player who has the most points in order to slow his climb to victory. In Smallworld, players who have diligently kept track of the distribution of victory points will prefer to attack the player who has the most.

But games must carefully balance the effect of a player’s own decisions on his standing against the effects of other players’ decisions on his standings. Depending on the length of the game and the number of opportunities for player interaction, strategic choices can be completely washed out by targeted player interaction’s damping effect. If skillful decisions ultimately do not significantly increase a player’s odds of winning due to inevitable restraint by other players, then by definition, the game incurs a high amount of luck. As in the example of the token-taking game, the player who wins, ultimately, will be almost entirely determined by arbitrary factors such as turn order, dice, or card draw. Therefore, if the purpose of a game is to challenge players with difficult decisions, targeted player interaction must be limited.

Kingmaking

“Kingmaking” scenarios, wherein the winner of the game is arbitrarily decided by one of the losers, are widely (although not universally) considered undesirable. The basic token taking game was an extreme example, in which nearly every decision by every player was partially arbitrary. Furthermore, the outcome of every game was decided arbitrarily by a player who lost. In general, Kingmaking decisions occur when a player faces targeted interactive decisions which don’t affect his own standing. Clearly Kingmaking is a phenomenon which can only arise in multiplayer games.

In more complex games, as long as there is some degree of targeted player interaction, kingmaking scenarios tends to arise. For instance, right at the end of a game, players are often “logically eliminated,” in that there is no chance they can win. But if these players can still modify the relative standing of other players, they will impact the outcome of the game in an arbitrary way.

Multiplayer Interaction in Context B: Realistic Play

Indeterminacy

As I have discussed before on this blog, all of the games we play have some indeterminacy, but most modern games limit the amount of indeterminacy so that players can feel as if they are in control of their fates and use inference to develop strategies. Therefore it is important to consider the indeterminacy which arises from multiplayer interaction. Even in Context A, where other players’ strategies are known by the other players due to their optimality, the element of multiplayer interaction can add indeterminacy by increasing the level of complexity of the game, thus expanding the game tree such that it stretches further beyond the limits of human cognitive processing (this is an example of Type III randomness, which I discussed in a previous post). Adding more players into a game exponentially increases the size of the game tree, and thus the heuristics we use to make decisions will generally become less faithful approximations to true optimal strategies.

In Context B, there arises another layer of indeterminacy due to the the fact that opponents’ strategies cannot be fully deduced, as they aren’t necessarily optimal. Decisions must be made with limited and unreliable information about opponents’ strategies, and thus the outcomes of these decisions are not fully known to the player who makes them. This is an example of Type 2.5 randomness (also discussed here). In two-player games, the decisions of only one opponent must be modeled with uncertainty. In a multiplayer game, a smaller proportion of the decisions in the game are made by each player, and therefore each player must model more opponents’ decisions with uncertainty. Furthermore, in a two player game, a player can use more information about the game state to model his opponents’ decisions. In a multiplayer game which proceeds in clockwise order, the opponent to a player’s left will make a decision with respect to a game state which is highly uncertain to that player. This phenomenon results in an element of indeterminacy which increases exponentially with the number of players.

As I have mentioned, players may act suboptimally in systematic ways such that their deviations from optimality are partially predictable, but these predictions come from information which is external to the game itself. Because the indeterminacy introduced into a game by multiplayer interaction is so agential, it may be difficult to control by the game designer.

Abuse

In a two player game, one stands to benefit from an opponent’s suboptimal moves for two reasons. The first reason is that suboptimal moves may be exploitable; by reacting appropriately to an opponent’s suboptimal move, a player can improve his standing. The second reason is that suboptimal moves do not have maximal utility, and therefore his opponent stands to passively benefit through increased odds of winning.

In a multiplayer games with targeted player interaction, this is not so straightforward. Very often, a suboptimal move will differently affect opponents in a way that an optimal move would not have. When a player’s deviation from optimal decision making causes him to interact more destructively with another player, this could be called abuse. (Admittedly, abuse has strong connotations for something which is often accidental and sometimes benign, but I don’t know of a softer word to describe this idea). For instance, if the strongest move for a player would be to attack opponent A, but he instead attacks opponent B, condemning both the player and opponent B to defeat by opponent A, opponent B has been abused. The effects of abuse and kingmaking are similar, but the causes are different. Kingmaking is caused by targeted interactive decisions made by a rational but indifferent player, whereas abuse is caused by truly suboptimal decisions. These suboptimal decisions will somewhat arbitrarily punish or reward other players due to the unpredictable variability of a player’s suboptimal decision making. The result is that in multiplayer games with non-perfect players, targeted player interaction can limit the amount of control a player has over his own standing.

There is also a potentially undesirable interaction between abuse and damping. In games which rely on targeted player interaction to dampen players’ standings, individual players have to act somewhat optimally in order to keep things competitive. Rubber-banding mechanisms can be unreliable if they depend on players acting in certain ways to function properly. When it is a player’s responsibility to reduce the standing of an opponent who is in the lead, but he instead engages in destructive interaction with another opponent, the actions of that suboptimal player can instead exacerbate the problem of a runaway leader. Similarly, mistargeted cooperative interaction can be indirectly abusive. A classic example is that in Settlers of Catan, players should avoid trading with players who are significantly in the lead, but short-sighted newbies will often do so anyways, thus indirectly abusing their other opponents and undermining an important damping structure in the game.

Politics

The authors of Characteristics of Games describe games which are essentially token taking games as “political games.” The most important decisions in these games involve whom to target, and the answer is generally “the person who is in the lead.” A player can, however, act as a political agent and convince an opponent to act on his behalf. But in Context A, wherein one’s opponents are rational agents, this kind of “table talk” wouldn’t make any difference – an optimal player will act optimally, and no amount of sweet talking or unofficial promises will sway her. Therefore I prefer to define politics as follows: politics is any form of exploitation which involves communication outside of one’s decision making. Threatening an opponent by moving your ships to his coastline would then not be considered politics, but telling him “if you trade with Russia, I will attack you” would be considered politics, if by doing so you convince that player to act on your behalf rather than engage in whatever move were optimal. A political game, then, would be one in which table talk and unofficial deal-making tend to emerge in Context B, that is, in real games with real players.

To some, politics can be a highly desirable trait in games. It can be immersive to attempt to influence other players through discussion in a way which thematically resembles real-life political wheeling and dealing. Diplomacy is a famously political game, where most of the gameplay is emergent secretive discussion, resulting in informal pacts and backstabbing. (In Context A, Diplomacy might look more like the token taking game, where with each action, perfect players could calculate how best to maintain a comfortable balance and would execute these moves without any need for discussion). In general, politics tends to emerge whenever there is targeted player interaction, because whenever a suboptimal player must choose an opponent to target, it is in his opponents’ interest to attempt to influence him, often through communication outside of the game itself.

But the politics in a game may sometimes be undesirable for two reasons. The first reason is that politics is an entirely Context B phenomenon, and thus highly agential. As a group of players increases in skill, the effectivity of political behavior may decrease, and thus political strategies can be transient. Because political activity takes place outside of the decision making within the game, it has more to do with the psychology and vulnerabilities of the humans themselves than the in-game decisions they have made up until this point. Heavily political games reward players who are skilled at manipulating and exploiting others psychologically or socially, and not necessarily players who have thoughtfully analyzed the game itself.

The second reason that politics may not be desirable is that the only way to introduce politics into a game is to face players with opportunities for targeted player interaction where it is not obvious whom it is better to target. This will encourage discussion amongst opponents to sway the player one way or the other, but it also directly introduces kingmaking or abuse into the game. If the correct coalitions to form and players to target is so obscure as to warrant dispassionate discussion, it is probably obscure enough that whomever is ultimately targeted will feel as if his fate is somewhat arbitrary.

Limiting Targeted Player Interaction

In the section “Incentive Structures,” I discussed how multiplayer games must have different kinds of rules than two-player games. Along these same lines, I would suggest that the ways in which players can interact with each other should be fundamentally different in multiplayer games compared with two player games. Adding mechanisms which allow for a great deal of player interaction in multiplayer games does not necessarily complement the existing mechanisms, but can in fact undermine them. The greater the amount of player interaction in a game, the more damping will occur, rendering early game decisions unimportant and thus rendering “thought redundant,” as expressed by Uwe Rosenberg in the quote at the beginning of the article. That player interaction introduces politics and the potential for abuse is less uniformly problematic, but rather a matter of taste. Rosenberg describes multiplayer aggression as being less “calculable” than aggression in two-player games, which I posit results from the exponentially increased indeterminacy of multiplayer games along with the potential for abuse.

Nonetheless, with few exceptions, modern multiplayer free-for-all board games all have some degree of interaction, and consequently exhibit some degree of damping, politics, kingmaking and abuse. My final argument is that these multiplayer games are successful in part due to the ways in which they control targeted player interaction, without eliminating player interaction entirely. There are two ways controlling targeted player interaction: either by restricting the nature and extent of player interaction, or through incentivization.

Restriction and Incentivization

Trivially, the amount of player interaction is restricted in every game (you generally aren’t allowed to throw your opponents’ pieces out the window at will). But I think a wonderful implementation of logically restricted player can be found in Richard Garfield’s King of Tokyo, which is a king-of-the-hill type game where one objective for players is to control the center of the board at their own peril. The rest of the players can only attack the player who is in Tokyo. This means that the player in Tokyo may superficially be the “target” of an attack, but the decision to be at risk was that of the attacked player. In this situation there is still targeted player interaction, because the attackers decision to attack with more or less force has more of an effect on the standing of the player in Tokyo than the other players. However, this restriction on whom a player can attack goes a long way to reduce the amount of agential damping, kingmaking, and abuse in the game. Similarly, games like Vampire: The Eternal Struggle, and Artifacts, Inc. restrict destructive and cooperative interaction (respectively) to the opponent to one’s left.

Restricting targeted player interaction through incentivization can be interpreted similarly. If a player has the means to attack another player, but she is indifferent as to her target, she will at best engage in damping by attacking the player in the lead, and at worst she will engage in abuse by attacking any other player. However, if attacking one opponent is particularly attractive because doing so yields a greater in-game reward, or if it is particularly inexpensive to attack an opponent because of his map position or lack of defenses, her target will be more predictable. Her target made decisions which resulted in his present lack of security; to some extent, he chose his targethood. This is similar to the example of King of Tokyo, where a player chooses to become a target by entering Tokyo.

Consider Smallworld, which is fundamentally a multiplayer war game. Players must choose which regions to conquer in order to maximize the points they get each round. Damping is present because if it is clear that one opponent is significantly ahead, players should prefer to conquer that opponent’s regions. However, the game heavily incentivizes the conquering of certain regions; players prefer to conquer certain types of regions due to their racial powers, and furthermore players can decide to disincentivize attack by occupying mountains, fortifying, or simply occupying undesirable regions. The peril of an opponent’s lead has to exceed a player’s competing incentives in order to invite damping, thus damping is limited by incentives.

Furthermore, these incentives reduce the prevalence of abuse and kingmaking. As I discussed, kingmaking occurs when players are indifferent as to whom to target, so adding incentives for players to target certain players can remove kingmaking from those decisions. Incentives also deter abuse, as they elucidate the correct target of a decision, making it less likely that a suboptimal player will choose the incorrect target.

Euro-style Games and Drafting

As an application of the concepts I have developed in this article, I would like look at an interactive general mechanism that is prevalent in modern games which are often considered to be Euro-style. Consider games in which players take turns claiming assets from a common pool. Examples of this mechanism include worker placement (Caylus, Agricola), in which the assets are actions and resources, card drafting (Seven Wonders, Blood Rage), in which the assets are cards, and games with rotating markets (Through the Ages, Suburbia). These mechanisms introduce player interaction into a game, because by taking an asset from the common pool one restricts and facilitates the decisions of one’s opponent.

The player interaction also tends to be targeted, for two reasons. When a player takes an asset from the common pool, his action most directly affects the player who is next. If there is a particularly large difference in value between the most valuable asset in the pool and the second most valuable asset, a player’s decision has the potential to greatly reward or punish the next player. Furthermore, the assets will have different values to different opponents due to context and specialization. Therefore, choosing certain assets may drastically affect certain opponents while barely affecting others. Damping is a possible here – a player may prefer to take a science card in 7 Wonders in order to prevent a leading opponent from finishing a set. Inevitably, abuse is possible, for instance when a player passes her boyfriend a desperately needed science card which she should have denied him.

But by engineering the value of the goods in the common pool to various players, games can limit targeting while still encouraging players to take into account the desires of their opponents. Consider the degree of specialization in the game, meaning the extent to which the value of the assets in the common pool differs from player to player. If the degree of specialization is too great, a player’s decisions will not need to be terribly sensitive to the desires of his opponents; the assets which benefit him benefit him alone. His opponents would be foolish to waste their time nabbing his preferred assets, and vice versa, except perhaps to engage in damping or abuse. If there is little to no specialization in a game, players will be less able to interfere with his opponents, but his decisions will not be not be informed by them either, so the benefits of player interaction will be largely lost. A game with this mechanism should balance the amount of specialization to encourage player interaction but limit undesirable artifacts of targeting.

Conclusion

From Chess to simulative American war games, board games have traditionally modeled combat. But generalizing combat from two players to multiple players has mathematical implications that should not be ignored. The type of indirect interaction often found of Eurogames may be partially explained by the political climate of Europe at the time when these games emerged, but their success is due to the way in which these games allow for multiple players while mitigating targeted player interaction and its undesirable consequences. In analyzing a game, we shouldn’t just ask “how much player interaction does this game have?” because a game with too much player interaction will degenerate into a token-taking analogue. We should ask “how does this game limit player interaction? What is the role of agential damping in this game? To what extent does this game allow or encourage abuse?” In future articles, I hope to discuss an information theoretical representation of player interaction, further discuss specialization and its relationship to player interaction, analyze player structures beyond 1v1 and free-for-alls, and perhaps discuss a generalization of interaction beyond interaction between players.

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