Nonmanipulable collective decision- making for games

This chapter explores a new approach that may be used in game development to help human players and/or non-player characters make collective decisions. We describe how previous work can be applied to allow game players to form a consensus from a simple range of possible outcomes in such a way that no player can manipulate it at the expense of the other players. We then extend that result and show how nonmanipulable consensus can be found in higher-dimensional outcome spaces. The results may be useful when developing artificial intelligence for non-player characters or constructing frameworks to aid cooperation among human players. INTRODUCTION Teamwork is important in many games. Whether they are human players or non-player characters (NPCs) or both, game entities must often work together to achieve goals. However, those goals do not always coincide perfectly, and, even when they do, players will not always agree on the best next course of action to take. Much research (see especially Rabin 2002, sec. 7) has explored effective decision-making for individual game agents, even in a multiagent context. By contrast, in this work, we assume that all agents have already individually decided which of the available outcomes (which are usually actions) they prefer over others, and we assume the agents desire to use those preferences to reach consensus for the group. For an example game situation, imagine a team of wargame players with a common goal: band together to attack the western coast of a continent held by a common enemy. They could attack the coast’s northernmost point, the southernmost point or anywhere in between, and each player has a different favorite attack point. If the players can be trusted to express sincere preferences, their preferred points could simply be averaged to give the consensus point. Averaging, however, can allow some players to gain a better outcome from their point of view by exaggerating their preferences, whereas other aggregation mechanisms may never reward such insincerity. When a group of players aims to benefit all members of the group by coordinating their actions, a method of combining their preferences into a single outcome is useful, but the usefulness may disappear if individual players can manipulate the outcome by expressing insincere preferences. Here we present a set of nonmanipulable collective-decision-making methods that apply to a wide range of game situations. In the sections below we review previous work that informs ours, look at several game situations that motivate our approach and present the ideas that provide an innovative solution.