Related papers: When is tit-for-tat unbeatable?

We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show…

Tit-for-Tat strategy is a strategy in repeated two-player symmetric games which imitates the previous action of the opponent. We show that the Tit-for-Tat strategy is a zero-determinant strategy, which unilaterally equalizes the expected…

Imitation is simple behavior which uses successful actions of others in order to deal with one's own problems. Because success of imitation generally depends on whether profit of an imitating agent coincides with those of other agents or…

We construct a statistical ensemble of games, where in each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the…

Imitation sometimes achieves success in multi-agent situations even though it is very simple. In game theory, success of imitation has been characterized by unbeatability against other agents. Previous studies specified conditions under…

Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning…

Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…

We design games for truly concurrent bisimilarities, including strongly truly concurrent bisimilarities and branching truly concurrent bisimilarities, such as pomset bisimilarities, step bisimilarities, history-preserving bisimilarities and…

This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…

Infinitely repeated games can support cooperative outcomes that are not equilibria in the one-shot game. The idea is to make sure that any gains from deviating will be offset by retaliation in future rounds. However, this model of…

We introduce the concept of deformed zero-determinant strategies in repeated games. We then show that the Tit-for-Tat strategy in the repeated prisoner's dilemma game is a deformed zero-determinant strategy, which unilaterally equalizes the…

Parity games are simple infinite games played on finite graphs with a winning condition that is expressive enough to capture nested least and greatest fixpoints. Through their tight relationship to the modal mu-calculus, they are used in…

The main challenge of combinatorial game theory is to handle combinatorial chaos, if one player knows the strategy better than his opponent, he is able to determine the exact results of a game. If both players are qualified competitor, the…

Iterated Prisoner's Dilemma(IPD) is a well-known benchmark for studying the long term behaviors of rational agents, such as how cooperation can emerge among selfish and unrelated agents that need to co-exist over long term. Many well-known…

In this paper, we study the notion of admissibility for randomised strategies in concurrent games. Intuitively, an admissible strategy is one where the player plays `as well as possible', because there is no other strategy that dominates…

Repeated games have a long tradition in the behavioral sciences and evolutionary biology. Recently, strategies were discovered that permit an unprecedented level of control over repeated interactions by enabling a player to unilaterally…

Evolutionary game theory has been an important tool for describing economic and social behaviour for decades. Approximate mean value equations describing the time evolution of strategy concentrations can be derived from the players'…

Two-player win/lose games of infinite duration are involved in several disciplines including computer science and logic. If such a game has deterministic winning strategies, one may ask how simple such strategies can get. The answer may…

This paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections…