A characterisation of the perfect equilibria of infinite horizon games

I introduce axiomatically infinite sequential games that extend Kuhn’s classical framework. Infinite games allow for (a) imperfect information, (b) an infinite horizon, and (c) infinite action sets. A generalized backward induction (GBI) procedure is defined for all such games over the roots of subgames. A strategy profile that survives backward pruning is called a backward induction solution (BIS). The main result of this paper finds that, similar to finite games of perfect information, the sets of BIS and subgame perfect equilibria (SPE) coincide for both pure strategies and for behavioral strategies that satisfy the conditions of finite support and finite crossing. Additionally, I discuss five examples of well-known games and political economy models that can be solved with GBI but not classic backward induction (BI). The contributions of this paper include (a) the axiomatization of a class of infinite games, (b) the extension of backward induction to infinite games, and (c) the proof that BIS and SPEs are identical for infinite games.

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INNOVATION AND FOREIGN INVESTMENT IN A DYNAMIC OLIGOPOLY

International Game Theory Review ◽

10.1142/s0219198900000032 ◽

2000 ◽

Vol 02 (01) ◽

pp. 1-28 ◽

Cited By ~ 8

Author(s):

MARIA-LUISA PETIT ◽

FRANCESCA SANNA-RANDACCIO ◽

BOLESLAW TOLWINSKI

Keyword(s):

Imperfect Competition ◽

Infinite Horizon ◽

Dynamic Game ◽

Innovation Process ◽

Analytical Techniques ◽

Computational Procedure ◽

International Strategy ◽

Changes Over Time ◽

The Impact ◽

Perfect Equilibria

The paper examines the impact of the firms' choice between export and foreign direct investment on the incentive to innovate, as well as the effects of innovation and technological spillovers on the firms' international strategy and on its changes over time. The innovation process is analysed in the context of a two-country imperfect competition market, modelled as an infinite horizon, non-linear dynamic game, for which Markov perfect equilibria are computed. Where the models are not tractable by analytical techniques, equilibria are calculated by using a computational procedure based on a policy iteration method.

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Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting

Mathematical Structures in Computer Science ◽

10.1017/s0960129515000365 ◽

2015 ◽

Vol 27 (5) ◽

pp. 751-761 ◽

Cited By ~ 6

Author(s):

SAMSON ABRAMSKY ◽

VIKTOR WINSCHEL

Keyword(s):

Game Theory ◽

Infinite Horizon ◽

Infinite Games ◽

Adequate Treatment ◽

Infinite Systems ◽

Deviation Principle ◽

Game Trees ◽

Subgame Perfect Equilibria ◽

Perfect Equilibria ◽

Extensive Games

We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame-perfect equilibria using a novel proof principle of predicate coinduction which is shown to be sound. We characterize all subgame-perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the pay-offs which amount to discounting the future. In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics.

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Dynamic games with (almost) perfect information

Theoretical Economics ◽

10.3982/te2927 ◽

2020 ◽

Vol 15 (2) ◽

pp. 811-859

Author(s):

Wei He ◽

Yeneng Sun

Keyword(s):

Dynamic Games ◽

Pure Strategy ◽

Infinite Horizon ◽

Complete Information ◽

Perfect Information ◽

State Variables ◽

Deterministic Dynamic ◽

Upper Hemicontinuity ◽

Subgame Perfect Equilibria ◽

Perfect Equilibria

This paper aims to solve two fundamental problems on finite‐ or infinite‐horizon dynamic games with complete information. Under some mild conditions, we prove the existence of subgame‐perfect equilibria and the upper hemicontinuity of equilibrium payoffs in general dynamic games with simultaneous moves (i.e., almost perfect information), which go beyond previous works in the sense that stagewise public randomization and the continuity requirement on the state variables are not needed. For alternating move (i.e., perfect‐information) dynamic games with uncertainty, we show the existence of pure‐strategy subgame‐perfect equilibria as well as the upper hemicontinuity of equilibrium payoffs, extending the earlier results on perfect‐information deterministic dynamic games.

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