We study a stochastic differential game between two insurance companies who employ reinsurance to reduce the risk of exposure. Under the assumption that the companies have large insurance portfolios compared to any individual claim size, their surplus processes can be approximated by stochastic differential equations. We formulate competition between the two companies as a game with a single pa...

Stochastic differential games are considered in a non-Markovian setting. Typically, in stochastic differential games the modulating process of the diffusion equation describing the state flow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB met...

We study the complexity of computing Nash equilibria in games where players arranged as the vertices of a graph play a symmetric 2-player game against their neighbours. We call this a pairwise interaction game. We analyse this game for n players with a fixed number of actions and show that (1) a mixed Nash equilibrium can be computed in constant time for any game, (2) a pure Nash equilibrium ca...

We consider the problem of finding stationary Nash equilibria (NE) in a finite discounted general-sum stochastic game. We first generalize a non-linear optimization problem from [9] to a general N player game setting. Next, we break down the optimization problem into simpler sub-problems that ensure there is no Bellman error for a given state and an agent. We then provide a characterization of ...

An imitation game is a finite two person normal form game in which the two players have the same set of pure strategies and the goal of the second player is to choose the same pure strategy as the first player. Gale et al. (1950) gave a way of passing from a given two person game to a symmetric game whose symmetric Nash equilibria are in oneto-one correspondence with the Nash equilibria of the ...

We examine the coalition-proof equilibria of a participation game in a public good mechanism and study which Nash equilibria are achieved through the cooperative behavior of agents. The participation game may have multiple Nash equilibria, and various numbers of participants may be attained at the Nash equilibria. We provide sufficient conditions for the Nash equilibrium of the participation ga...

Noncooperative game theory provides a norma­ tive framework for analyzing strategic interactions. However, for the toolbox to be operational, the so­ lutions it defines will have to be computed. In this paper, we provide a single reduction that 1) demon­ strates -hardness of determining whether Nash equilibria with certain natural properties exist, and 2) demonstrates the -hardness of counting ...

In his dissertation of 1950, Nash based his concept of solution to a game on the principles that “a rational prediction should be unique, that the players should be able to deduce and make use of it.” In this paper, we address the issue of when such definitive solutions are possible. We assume player rationality at least as strong as Aumann’s rationality. By formalizing Nash’s reasoning, we sho...