This note studies contests in which multiple participants compete for two distinct prizes. The participants have distinct constant marginal costs, which are commonly known. We show that the contests have a unique Nash equilibrium, and we characterize the equilibrium payoffs and strategies in...

The literature on the computation of Nash equilibria in n-person games is dominated by simplicial methods. This paper is the first to introduce a globally convergent algorithm that fully exploits the differentiability present in the problem. It presents an everywhere differentiable homotopy to...

There are situations in which competitors ally to pursue a common objective. This simultaneous presence of cooperation and competition is called coopetition and we study it theoretically and experimentally in a group contest setup. More concretely, we analyze a group contest with a new sharing...

This paper examines a class of three-agent games with a principal and two identical agents. The role of the principal is to facilitate efficient outcomes for the two agents which are not feasible in his absence. Our results show that imposing a mediator or "facilitator" on "any" two person...

The implausibility of the extreme rationality assumptions of Nash equilibrium has been attested by numerous experimental studies with human players. In particular, the fundamental social dilemmas such as the Traveler's dilemma, the Prisoner's dilemma, and the Public Goods game demonstrate high...

Some results in the monotone comparative statics literature tell us that if a parameter increases, some old equilibria are smaller than some new equilibria. We give a sufficient condition such that at a new parameter value every old equilibrium is smaller than every new equilibrium. We also...

Is civil and criminal litigation a search for truth, like science or philosophy, or a game of skill and luck, like the game of poker? Although the process of litigation has been modeled as a Prisoner’s Dilemma, as a War of Attrition, as a Game of Chicken, and even as a simple coin toss, no one...

We construct a Cournot model in which firms have uncertainty about the total number of firms in the industry. We model such an uncertainty as a Poisson game and we characterize the set of equilibria after deriving some novel properties of the Poisson distribution. When the marginal cost is...

Theoretical and experimental studies of noncooperative games increasingly recognize Nash equilibrium as a limiting outcome of players repeated interaction. This note, while sharing that view, illustrates and advocates combined use of convex optimization and differential equations, the purpose...

We prove the existence of a pure-strategy trembling-hand perfect equilibrium in upper semicontinuous potential games, and we show that generic potential games possess pure-strategy strictly perfect and essential equilibria. We also establish a more powerful result: the set of maximizers of an...