scholarly journals Dynamic games with (almost) perfect information

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.

On the Strategic Equivalence of Linear Dynamic and Repeated Games

2015 ◽  
Vol 17 (03) ◽  
pp. 1550006
Author(s):  
Joachim Hubmer
Keyword(s):  
Repeated Games ◽  
Dynamic Game ◽  
Repeated Game ◽  
Transition Function ◽  
The State ◽  
State Variables ◽  
Equivalent Representation ◽  
Deterministic Dynamic ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

Dynamic (or stochastic) games are, in general, considerably more complicated to analyze than repeated games. This paper shows that for every deterministic dynamic game that is linear in the state, there exists a strategically equivalent representation as a repeated game. A dynamic game is said to be linear in the state if it holds for both the state transition function as well as for the one-period payoff function that (i) they are additively separable in action profiles and states and (ii) the state variables enter linearly. Strategic equivalence refers to the observation that the two sets of subgame perfect equilibria coincide, up to a natural projection of dynamic game strategy profiles on the much smaller set of repeated game histories. Furthermore, it is shown that the strategic equivalence result still holds for certain stochastic elements in the transition function if one allows for additional signals in the repeated game or in the presence of a public correlating device.

scholarly journals Subgame‐perfect equilibrium in games with almost perfect information: Dispensing with public randomization

2021 ◽  
Vol 16 (4) ◽  
pp. 1221-1248
Author(s):  
Paulo Barelli ◽  
John Duggan
Keyword(s):  
Dynamic Games ◽  
Subgame Perfect Equilibrium ◽  
Perfect Information ◽  
State Transitions ◽  
Original Game ◽  
Equilibrium Existence ◽  
Weakly Continuous ◽  
Continuous State ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

Harris, Reny, and Robson (1995) added a public randomization device to dynamic games with almost perfect information to ensure existence of subgame perfect equilibria (SPE). We show that when Nature's moves are atomless in the original game, public randomization does not enlarge the set of SPE payoffs: any SPE obtained using public randomization can be “decorrelated” to produce a payoff‐equivalent SPE of the original game. As a corollary, we provide an alternative route to a result of He and Sun (2020) on existence of SPE without public randomization, which in turn yields equilibrium existence for stochastic games with weakly continuous state transitions.

ON THE COMPENSATION OF IMPERFECT INFORMATION IN DYNAMIC GAMES

2000 ◽  
Vol 02 (02n03) ◽  
pp. 229-248 ◽  
Author(s):  
JOSEF SHINAR ◽  
TAL SHIMA ◽  
VALERY Y. GLIZER
Keyword(s):  
Optimal Strategy ◽  
Information Structure ◽  
Dynamic Games ◽  
Imperfect Information ◽  
Substantial Improvement ◽  
Perfect Information ◽  
Lateral Acceleration ◽  
Position Vector ◽  
State Variables ◽  
Delayed Information

A linear pursuit-evasion game with first-order acceleration dynamics and bounded controls is considered. In this game, the pursuer has to estimate the state variables of the game, including the lateral acceleration of the evader, based on the noise-corrupted measurements of the relative position vector. The estimation process inherently involves some delay, rendering the information structure of the pursuer imperfect. If the pursuer implements the optimal strategy of the perfect information game, an evader with perfect information can take advantage of the estimation delay. However, the performance degradation is minimised if the pursuer compensates for its own estimation delay by implementing the optimal strategy derived from the solution of the imperfect (delayed) information game. In this paper the analytical solution of the delayed information game, allowing to predict the value of the game, is presented. The theoretical results are tested in a noise-corrupted scenario by Monte Carlo simulations, using a Kalman filter type estimator. The simulation results confirm the substantial improvement achieved by the new pursuer strategy.

scholarly journals Generalized Backward Induction: Justification for a Folk Algorithm

Games ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 34
Author(s):  
Marek Mikolaj Kaminski
Keyword(s):  
Imperfect Information ◽  
Infinite Horizon ◽  
Backward Induction ◽  
Behavioral Strategies ◽  
Infinite Games ◽  
Sequential Games ◽  
Finite Games ◽  
Pure Strategies ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

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.

scholarly journals Interactive Information Design

2021 ◽  
Author(s):  
Frédéric Koessler ◽  
Marie Laclau ◽  
Tristan Tomala
Keyword(s):  
Pure Strategy ◽  
Simple Game ◽  
Public Information ◽  
Compact Set ◽  
Countable Support ◽  
Normal Form Game ◽  
Statistical Experiments ◽  
Correlated Equilibria ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

We study the interaction between multiple information designers who try to influence the behavior of a set of agents. When each designer can choose information policies from a compact set of statistical experiments with countable support, such games always admit subgame-perfect equilibria. When designers produce public information, every equilibrium of the simple game in which the set of messages coincides with the set of states is robust in the sense that it is an equilibrium with larger and possibly infinite and uncountable message sets. The converse is true for a class of Markovian equilibria only. When designers produce information for their own corporation of agents, robust pure-strategy equilibria exist and are characterized via an auxiliary normal-form game in which the set of strategies of each designer is the set of outcomes induced by Bayes correlated equilibria in her corporation.

scholarly journals Voting behavior under outside pressure: promoting true majorities with sequential voting?

2021 ◽  
Author(s):  
Friedel Bolle ◽  
Philipp E. Otto
Keyword(s):  
Voting Behavior ◽  
Subgame Perfect Equilibrium ◽  
Complete Information ◽  
Emotional Reactions ◽  
Equilibrium Strategy ◽  
Perfect Equilibrium ◽  
Roll Call ◽  
Sequential Voting ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

AbstractWhen including outside pressure on voters as individual costs, sequential voting (as in roll call votes) is theoretically preferable to simultaneous voting (as in recorded ballots). Under complete information, sequential voting has a unique subgame perfect equilibrium with a simple equilibrium strategy guaranteeing true majority results. Simultaneous voting suffers from a plethora of equilibria, often contradicting true majorities. Experimental results, however, show severe deviations from the equilibrium strategy in sequential voting with not significantly more true majority results than in simultaneous voting. Social considerations under sequential voting—based on emotional reactions toward the behaviors of the previous players—seem to distort subgame perfect equilibria.

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

2015 ◽  
Vol 27 (5) ◽  
pp. 751-761 ◽  
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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