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Is there a joint distribution of $n$ random variables over the natural numbers, such that they always form an increasing sequence and whenever you take two subsets of the set of random variables of the same cardinality, their distribution…
We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a)…
We study the two-player safe game of Competitive Diffusion, a game-theoretic model for the diffusion of technologies or influence through a social network. In game theory, safe strategies are mixed strategies with a minimal expected gain…
Toral introduced so-called cooperative Parrondo games, in which there are N players (3 or more) arranged in a circle. At each turn one player is randomly chosen to play. He plays either game A or game B, depending on the strategy. Game A…
Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two…
The problem of dividing resources fairly occurs in many practical situations and is therefore an important topic of study in economics. In this paper, we investigate envy-free divisions in the setting where there are multiple players in…
This work shows that the formation of a finite number of coalitions in a nonatomic network congestion game benefits everyone. At the equilibrium of the composite game played by coalitions and individuals, the average cost to each coalition…
Many studies have shown that humans are "predictably irrational": they do not act in a fully rational way, but their deviations from rational behavior are quite systematic. Our goal is to see the extent to which we can explain and justify…
The very notion of social network implies that linked individuals interact repeatedly with each other. This allows them not only to learn successful strategies and adapt to them, but also to condition their own behavior on the behavior of…
Involution now refers to the phenomenon that competitors in the same field make more efforts to struggle for limited resources but get lower individual ''profit effort ratio''. In this work, we investigate the evolution of the involution…
TheMinority Game (MG) has become a paradigm to probe complex social and economical phenomena where adaptive agents compete for a limited resource, and it finds applications in statistical and nonlinear physics as well. In the traditional MG…
Game-theoretic probability uses the structure of gambles to define a concept like probability, but which is more flexible and robust. We show that results in game-theoretic probability can be thought of as minimax theorems for specific…
We show that for any $\epsilon>0$, as the number of agents gets large, the share of games that admit a pure $\epsilon$-equilibrium converges to 1. Our result holds even for pure $\epsilon$-equilibrium in which all agents, except for at most…
We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus.…
Game theory has been increasingly applied in settings where the game is not known outright, but has to be estimated by sampling. For example, meta-games that arise in multi-agent evaluation can only be accessed by running a succession of…
Classical game theory is a powerful framework to analyze the strategic interactions among rational players. However, in many real-life scenarios, players choose actions based on their inherent natural tendencies rather than deliberate…
In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…
Over a century ago, Oliver Wendell Holmes invited scholars to look at the law through the lens of probability theory: "The prophecies of what the courts will do in fact, and nothing more pretentious, are what I mean by the law." Yet few…
The game of best choice (or "secretary problem") is a model for making an irrevocable decision among a fixed number of candidate choices that are presented sequentially in random order, one at a time. Because the classically optimal…
What is the physical origin of player cooperation in minority game? And how to obtain maximum global wealth in minority game? We answer the above questions by studying a variant of minority game from which players choose among $N_c$…