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This paper focuses on the performance of equalizer zero-determinant (ZD) strategies in discounted repeated Stackerberg asymmetric games. In the leader-follower adversarial scenario, the strong Stackelberg equilibrium (SSE) deriving from the…

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…

The iterated prisoner's dilemma is a game that produces many counter-intuitive and complex behaviors in a social environment, based on very simple basic rules. It illustrates that cooperation can be a good thing even in a competitive world,…

Gameplay under various forms of uncertainty has been widely studied. Feldman et al. (2010) studied a particularly low-information setting in which one observes the opponent's actions but no payoffs, not even one's own, and introduced an…

Evolutionary game theory, encompassing discrete, continuous, and mixed strategies, is pivotal for understanding cooperation dynamics. Discrete strategies involve deterministic actions with a fixed probability of one, whereas continuous…

It is well known that in contrast to the Prisoner's Dilemma, the snowdrift game can lead to a stable coexistence of cooperators and cheaters. Recent theoretical evidence on the snowdrift game suggests that gradual evolution for individuals…

Human decision behaviour is quite diverse. In many games humans on average do not achieve maximal payoff and the behaviour of individual players remains inhomogeneous even after playing many rounds. For instance, in repeated prisoner…

Strategy changes are an essential part of evolutionary games. Here we introduce a simple rule that, depending on the value of a single parameter $w$, influences the selection of players that are considered as potential sources of the new…

In an iterated two-person game, for instance prisoner's dilemma or the snowdrift game, there exist strategies that force the payoffs of the opponents to be equal. These equalizer strategies form a subset of the more general zero-determinant…

Mixed extension has played an important role in game theory, especially in the proof of the existence of Nash equilibria in strategic form games. Mixed extension can be regarded as continuous relaxation of a strategic form game. Recently,…

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma, namely the Prisoner's Dilemma. Specifically, for a…

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…

Behavioral experiments on the ultimatum game (UG) reveal that we humans prefer fair acts, which contradicts the prediction made in orthodox Economics. Existing explanations, however, are mostly attributed to exogenous factors within the…

Game theory provides a quantitative framework for analyzing the behavior of rational agents. The Iterated Prisoner's Dilemma in particular has become a standard model for studying cooperation and cheating, with cooperation often emerging as…

Learning from a partner who collects higher payoff is a frequently used working hypothesis in evolutionary game theory. One of the alternative dynamical rules is when the focal player prefers to follow the strategy choice of the majority in…

Evolutionary game theory assumes that players replicate a highly scored player's strategy through genetic inheritance. However, when learning occurs culturally, it is often difficult to recognize someone's strategy just by observing the…

Repeated interactions are ubiquitous and known to promote social behaviour. While research often focuses on cooperation in the Prisoner's Dilemma, experimental evidence suggests repeated interactions also foster fairness. This study…

Repeated game has long been the touchstone model for agents' long-run relationships. Previous results suggest that it is particularly difficult for a repeated game player to exert an autocratic control on the payoffs since they are jointly…

Using semi-tensor product (STP) of matrices, the profile evolutionary equation (PEE) for repeated finite games is obtained. By virtue of PEE, the zero-determinant (ZD) strategies are developed for general finite games. A formula is then…

Consider a system in which players at nodes of an underlying graph G repeatedly play Prisoner's Dilemma against their neighbors. The players adapt their strategies based on the past behavior of their opponents by applying the so-called…