Epstein (1998) demonstrates that in the demographic Prisoner's Dilemma game it is possible to sustain cooperation in a repeated game played on a finite grid, where agents are spatially distributed and of fixed strategy type ('cooperate' or 'defect'). We introduce a methodology to formalize the...

A distributed system model is studied, where individual agents play repeatedly against each other and change their strategies based upon previous play. It is shown how to model this environment in terms of continuous population densities of agent types. A complication arises because the...

We propose a meta-heuristic approach for solving nonlinear dynamic tracking games. In contrast to more "traditional" methods based on linear-quadratic (LQ) techniques, this derivative-free method is very flexible (e.g. to introduce inequality constraints). The meta-heuristic is applied to a...

We construct subgame-perfect equilibria with mixed strategies for symmetric stochastic timing games with arbitrary strategic incentives. The strategies are qualitatively different for local first- or second-mover advantages, which we analyse in turn. When there is a local second-mover advantage,...

In this paper we analyse a dynamic model of investment under uncertainty in a duopoly, in which each firm has an option to switch from the present market to a new market. We construct a subgame perfect equilibrium in mixed strategies and show that both preemption and attrition can occur along...

We consider a basic stochastic evolutionary model with rare mutation and a best-reply (or better-reply) selection mechanism. Following Young's papers, we call a state stochastically stable if its long-term relative frequency of occurrence is bounded away from zero as the mutation rate decreases...

Unique-lowest sealed-bid auctions are auctions in which participation is endogenous and the winning bid is the lowest bid among all unique bids. Such auctions admit very many Nash equilibria (NEs) in pure and mixed strategies. The two-bidders' auction is similar to the Hawk-Dove game, which...

Outcomes of the shallow lake interest conflict are presented in a number of different contexts: quasi-static and dynamic social planning, and quasi-static one-shot and repeated non-cooperative play. As the underlying dynamics are non-convex, the analysis uses geometrical-numerical methods: the...

We propose a new methodology exploring Markov perfect equilibrium strategies in differential games with regime switching. Specifically, we develop a general game with two players having two kinds of strategies. Players choose an action that influences the evolution of a state variable, and...

Dynamic decision-making without commitment is usually modelled as a game between the current and future selves of the decision maker. It has been observed that if the time-horizon is infinite, then such games may have multiple subgame-perfect equilibrium solutions. We provide a sufficient...