Infinite Horizon Dynamic Games Research Articles

Mowing the grass

Mowing the grass is a cyclical pattern in counterterrorism campaigns where governments attack to destroy terrorist capacity, thereby achieving a period of quiet as groups recover. If groups expect their capacity to be destroyed, why build their capabilities in the first place? I analyze an infinite-horizon dynamic game where a group endogenously builds capacity in the face of potential attacks and capacity is an evolving, persistent variable. The model highlights that terrorist groups and governments have incentives to create strategic uncertainty and thus explains attack cycles without punishment strategies, revenge preferences or imperfect/incomplete information. I calibrate the model to time-series data in the Israeli–Palestinian conflict describing rockets fired from Gaza. The results illustrate a peace-making dilemma: altering the government’s incentives will have comparatively minimal effects on long-term conflict dynamics, whereas changing the terrorists’ incentives to acquire capacity would either increase the frequency of high-capacity terrorism or government attacks.

A note on payments in the lab for infinite horizon dynamic games with discounting

A note on payments in the lab for infinite horizon dynamic games with discounting

The Stackelberg Games of Water Extraction with Myopic Agents

We consider a discrete-time, infinite-horizon dynamic game of groundwater extraction. A Water Agency charges an extraction cost to water users and controls the marginal extraction cost so that it depends not only on the level of groundwater but also on total water extraction (through a parameter [Formula: see text] that represents the degree of strategic interactions between water users) and on rainfall (through parameter [Formula: see text]). The water users are selfish and myopic, and the goal of the agency is to give them incentives so as to improve their total discounted welfare. We look at this problem in several situations. In the first situation, the parameters [Formula: see text] and [Formula: see text] are considered to be fixed over time. The first result shows that when the Water Agency is patient (the discount factor tends to 1), the optimal marginal extraction cost asks for strategic interactions between agents. The contrary holds for a discount factor near 0. In a second situation, we look at the dynamic Stackelberg game where the Agency decides at each time what cost parameter they must announce. We study theoretically and numerically the solution to this problem. Simulations illustrate the possibility that threshold policies are good candidates for optimal policies.

Infinite Horizon Dynamic Games: A New Approach via Information Updating

This paper formulates a new approach to analyze infinite horizon dynamic games with uncertainties and unknowns in the players’ future payoff structures. In many game situations, the game horizon would last for an indefinitely long period and one has to consider them as infinite horizon games. Existing infinite horizon dynamic games often rely on the assumption of time-invariant game structures for the derivation of equilibrium solutions. However, many events in the considerably far future are intrinsically unknown. In this paper, information about the players’ future payoffs will be revealed as the game proceeds. Making use of the newly obtained information, the players revise their strategies accordingly, and the process will continue indefinitely. This new approach for the analysis of infinite horizon dynamic games via information updating provides a more realistic and practical alternative to the study of infinite horizon dynamic games.

Interim correlated rationalizability in infinite games

In a Bayesian game, assume that the type space is a complete, separable metric space, the action space is a compact metric space, and the payoff functions are continuous. We show that the iterative and fixed-point definitions of interim correlated rationalizability (ICR) coincide, and ICR is non-empty-valued and upper hemicontinuous. This extends the finite-game results of Dekel et al. (2007), who introduced ICR. Our result applies, for instance, to discounted infinite-horizon dynamic games.

In This Issue

In This Issue

Sequential Correlated Equilibria in Stopping Games

In many situations, such as trade in stock exchanges, agents have many opportunities to act within a short interval of time. The agents in such situations can often coordinate their actions in advance, but coordination during the game consumes too much time. An equilibrium in such situations has to be sequential in order to handle mistakes made by players. In this paper, we present a new solution concept for infinite-horizon dynamic games, which is appropriate for such situations: a sequential normal-form correlated approximate equilibrium. Under additional assumptions, we show that every such game admits this kind of equilibrium.

Markov Perfect Equilibrium Existence for a Class of Undiscounted Infinite-Horizon Dynamic Games

We prove the existence of Markov perfect equilibria (MPE) for nonstationary undiscounted infinite-horizon dynamic games with alternating moves. A suitable finite-horizon equilibrium relaxation, the ending state constrained MPE, captures the relevant features of an infinite-horizon MPE for a long enough horizon, under a uniformly bounded reachability assumption.

Capital accumulation and income distribution as the outcome of a dynamic game

This paper presents a model of an economy with two representative agents (a capitalist and a worker) who play an infinite-horizon dynamic game about income distribution. We consider three types of equilibria, which correspond to joint price-taking (Walrasian equilibrium) and to wage-setting by either the capitalist (capitalistic equilibrium) or the worker (laborist equilibrium). For the last two of them, an inefficient feedback Stackelberg solution is first analyzed. Afterwards we apply a version of the Folk theorem and obtain a wide range of sustainable efficient equilibria, one of which coincides with the Nash bargaining solution.

Technology sharing cartels and industrial structure

The effects of “technology sharing cartels” on the behavior of firms and industrial structure are analyzed. Unit production costs are assumed to decrease with experience, which at any given time is proportional to the total production accumulated until that time. The “learning by doing” process is examined in a context of a duopolistic market, modeled as an infinite horizon dynamic game, for which subgame perfect (feedback) Nash equilibria are sought. Both symmetric and asymmetric oligopolies are examined. Since the models are non-linear and intractable by analytical techniques, equilibria are computed by using a computational procedure based on a policy iteration method.

A folk theorem for dynamic games

This paper focuses on infinite horizon dynamic games satisfying the monotonicity property: the objective function of every player is increasing (decreasing) in the strategy of the other players. We prove that, when closed-loop strategies are allowed, the set of Nash equilibrium payoffs coincides with the set of individually rational feasible payoffs in the game which allows only open-loop strategies. The significance of this general result is demonstrated by illustrating its applicability to the study of dynamic duopolistic competition [Fershtman and Kamien (1987), Reynolds (1987)], dynamic voluntary provision of public goods [Fershtman and Nitzan (1991)] and competitive arms race [Van der Ploeg and De Zeeuw (1990)].

Perfect equilibrium in non-randomized strategies in a class of symmetric dynamic games

This paper considers a class of infinite-horizon dynamic games that has immediate application to problems stemming from the oligopolistic exploitation of (renewable or non-renewable) common property resources. Under a symmetry assumption on the payoff structure, it is shown that the game admits a subgameperfect equilibrium in non-randomized Markovian strategies. These equilibrium strategies possess certain strong regularity properties which facilitate characterization of equilibrium play. Stationary equilibria are not Pareto-optimal in a convex environment. Additionally, such equilibria necessarily result in monotonic trajectories.