Related papers: Numerical Asymptotic Results in Game Theory Using …
We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…
We present a method of backward induction for computing approximate subgame perfect Nash equilibria of infinitely repeated games with discounted payoffs. This uses the selection monad transformer, combined with the searchable set monad…
Zero-sum stochastic games generalize the notion of Markov Decision Processes (i.e. controlled Markov chains, or stochastic dynamic programming) to the 2-player competitive case : two players jointly control the evolution of a state…
Classical objectives in two-player zero-sum games played on graphs often deal with limit behaviors of infinite plays: e.g., mean-payoff and total-payoff in the quantitative setting, or parity in the qualitative one (a canonical way to…
So far, the theory of equilibrium selection in the infinitely repeated prisoner's dilemma is insensitive to communication possibilities. To address this issue, we incorporate the assumption that communication reduces -- but does not…
We study deterministic games of infinite duration played on graphs and focus on the strategy complexity of quantitative objectives. Such games are known to admit optimal memoryless strategies over finite graphs, but require infinite-memory…
In several standard models of dynamic programming (gambling houses, MDPs, POMDPs), we prove the existence of a very robust notion of value for the infinitely repeated problem, namely the pathwise uniform value. This solves two open…
We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives…
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…
We generalize the quantum Prisoner's Dilemma to the case where the players share a non maximally entangled states. We show that the game exhibits an intriguing structure as a function of the amount of entanglement with two thresholds which…
The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the…
Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world…
A temporal-theoretic formalism for understanding game theory is described where a strict ordering relation on a set of time points $T$ defines a game on $T$. Using this formalism, a proof of Zermelo's Theorem, which states that every finite…
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…
Compositional Game Theory is a new, recently introduced model of economic games based upon the computer science idea of compositionality. In it, complex and irregular games can be built up from smaller and simpler games, and the equilibria…
We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…
We present a new approach to solving games with a countably or uncountably infinite number of players. Such games are often used to model multiagent systems with a large number of agents. The latter are frequently encountered in economics,…
We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). Formally, we prove lower bounds against the accuracy of FPC-interpretations that map Unique…
Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we…
We investigate evolutionary dynamics of altruism with long-range interaction on a cycle. The interaction between individuals is described by a simplified version of the prisoner's dilemma (PD) game in which the payoffs are parameterized by…