Related papers: Capital Games and Growth Equilibria
Gambles are random variables that model possible changes in monetary wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes.…
A notion of incentive for agents is introduced which leads to a very general notion of an equilibrium for a finite game. Sufficient conditions for the existence of these equilibria are given. Known existence theorems are shown to be…
Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…
Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…
In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
The concept of power among players can be expressed as a combination of their utilities. A player who obeys another takes into account the utility of the dominant one. Technically it is a matter of superimposing some weighted sum or product…
We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…
We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
We introduce the concept of budget games. Players choose a set of tasks and each task has a certain demand on every resource in the game. Each resource has a budget. If the budget is not enough to satisfy the sum of all demands, it has to…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
We study financial systems from a game-theoretic standpoint. A financial system is represented by a network, where nodes correspond to firms, and directed labeled edges correspond to debt contracts between them. The existence of cycles in…
Economic ensembles can be modeled as networks of interacting agents whose be-haviors are described in terms of game theory. The evolutionary paradigm has been applied to two-person games to discover strategies in this context.…
We study graphs and two-player games in which rewards are assigned to states, and the goal of the players is to satisfy or dissatisfy certain property of the generated outcome, given as a mean payoff property. Since the notion of…
We propose a payoff function extending Minority Games (MG) that captures the competition between agents to make money. In constrast with previous MG, the best strategies are not always targeting the minority but are shifting…
We study the capital growth in gambling with (and without) side information and memory effects. We derive several equalities for gambling, which are of similar form to the Jarzynski equality and its extension to systems with feedback…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
This article introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features…
The core is a dominant solution concept in economics and cooperative game theory; it is predominantly used for profit, equivalently cost or utility, sharing. This paper demonstrates the versatility of this notion by proposing a completely…