Related papers: Unbeatable Tit-for-Tat as a Zero-Determinant Strat…
The recent discovery of zero-determinant strategies for the iterated Prisoner's Dilemma sparked a surge of interest in the surprising fact that a player can exert unilateral control over iterated interactions. These remarkable strategies,…
In two-player repeated games, Zero-Determinant (ZD) strategies enable a player to unilaterally enforce a linear payoff relation between her own and her opponent's payoff irrespective of the opponent's strategy. This manipulative nature of…
An oligopoly is a market in which the price of goods is controlled by a few firms. Cournot introduced the simplest game-theoretic model of oligopoly, where profit-maximizing behavior of each firm results in market failure. Furthermore, when…
Zero Determinant (ZD) strategies are a new class of probabilistic and conditional strategies that are able to unilaterally set the expected payoff of an opponent in iterated plays of the Prisoner's Dilemma irrespective of the opponent's…
In a single-state repeated game, zero-determinant strategies can unilaterally force functions of the payoffs to take values in particular closed intervals. When the explicit use of a determinant is absent from the analysis, they are instead…
We explore some strategies which tend to perform well in the IPD. We start off by showing the significance of Tit-For-Tat strategies in evolutionary game theory. This is followed by a theoretical derivation of zero-determinant strategies,…
Controlling payoffs in repeated games is one of the important topics in control theory of multi-agent systems. Recently proposed zero-determinant strategies enable players to unilaterally enforce linear relations between payoffs.…
Two-player games have had a long and fruitful history of applications stretching across the social, biological, and physical sciences. Most applications of two-player games assume synchronous decisions or moves even when the games are…
The theory of direct reciprocity explores how individuals cooperate when they interact repeatedly. In repeated interactions, individuals can condition their behaviour on what happened earlier. One prominent example of a conditional strategy…
The prisoner's dilemma describes a conflict between a pair of players, in which defection is a dominant strategy whereas cooperation is collectively optimal. The iterated version of the dilemma has been extensively studied to understand the…
Long-term cooperation, competition, or exploitation among individuals can be modeled through repeated games. In repeated games, Press and Dyson discovered zero-determinant (ZD) strategies that enforce a special relationship between two…
One of the most important questions in game theory concerns how mutual cooperation can be achieved and maintained in a social dilemma. In Axelrod's tournaments of the iterated prisoner's dilemma, Tit-for-Tat (TFT) demonstrated the role of…
Researchers have explored the performance of Iterated Prisoner's Dilemma strategies for decades, from the celebrated performance of Tit for Tat to the introduction of the zero-determinant strategies and the use of sophisticated learning…
Recent theory shows that extortioners taking advantage of the zero-determinant (ZD) strategy can unilaterally claim an unfair share of the payoffs in the Iterated Prisoner's Dilemma. It is thus suggested that against a fixed extortioner,…
Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is…
Cooperation is usually represented as a Prisoner's Dilemma game. Although individual self-interest may not favour cooperation, cooperation can evolve if, for example, players interact multiple times adjusting their behaviour accordingly to…
Repeated game theory has been one of the most prevailing tools for understanding the long-run relationships, which are footstones in building human society. Recent works have revealed a new set of "zero-determinant (ZD)" strategies, which…
We study new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. We say that two games are "strategically equivalent" if, for every…
Strategic decision-making in uncertain and adversarial environments is crucial for the security of modern systems and infrastructures. A salient feature of many optimal decision-making policies is a level of unpredictability, or randomness,…
Indifference of a player with respect to two distinct outcomes of a game cannot be handled by small perturbations, because the actual choice may have significant impact on other players, and cause them to act in a way that has significant…