Related papers: Controlling conditional expectations by zero-deter…
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…
In iterated games, a player can unilaterally exert influence over the outcome through a careful choice of strategy. A powerful class of such "payoff control" strategies was discovered by Press and Dyson (2012). Their so-called…
Repeated games are useful models to analyze long term interactions of living species and complex social phenomena. Zero-determinant (ZD) strategies in repeated games discovered by Press and Dyson in 2012 enforce a linear payoff relationship…
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…
In repeated interactions between individuals, we do not expect that exactly the same situation will occur from one time to another. Contrary to what is common in models of repeated games in the literature, most real situations may differ a…
Direct reciprocity and conditional cooperation are important mechanisms to prevent free riding in social dilemmas. But in large groups these mechanisms may become ineffective, because they require single individuals to have a substantial…
Since the introduction of zero-determinant strategies, extortionate strategies have received considerable interest. While an interesting class of strategies, the definitions of extortionate strategies are algebraically rigid, apply only to…
We study zero-sum differential games with state constraints and one-sided information, where the informed player (Player 1) has a categorical payoff type unknown to the uninformed player (Player 2). The goal of Player 1 is to minimize his…
Repeated games are a framework for investigating long-term interdependence of multi-agent systems. In repeated games, zero-determinant (ZD) strategies attract much attention in evolutionary game theory, since they can unilaterally control…
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…
We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the…
A formula is presented for designing zero-determinant(ZD) strategies of general finite games, which have $n$ players and players can have different numbers of strategies. To this end, using semi-tensor product (STP) of matrices, the profile…
We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In this dynamics, a belief estimate of the parameter is repeatedly updated given players' strategies and realized…
Iterated games are a fundamental component of economic and evolutionary game theory. They describe situations where two players interact repeatedly and have the possibility to use conditional strategies that depend on the outcome of…
We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoff-relevant parameter. In each time step, the platform updates a belief estimate…
Direct reciprocity is a wide-spread mechanism for evolution of cooperation. In repeated interactions, players can condition their behavior on previous outcomes. A well known approach is given by reactive strategies, which respond to the…
We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform…
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…
Evolutionary game theory provides a mathematical foundation for cross-disciplinary fertilization, especially for integrating ideas from artificial intelligence and game theory. Such integration offers a transparent and rigorous approach to…
We consider the repeated prisoner's dilemma (PD). We assume that players make their choices knowing only average payoffs from the previous stages. A player's strategy is a function from the convex hull $\mathfrak{S}$ of the set of payoffs…