3,287 research outputs found
Subgame-Perfect Equilibria in Stochastic Timing Games
We introduce a notion of subgames for stochastic timing games and the related
notion of subgame-perfect equilibrium in possibly mixed strategies. While a
good notion of subgame-perfect equilibrium for continuous-time games is not
available in general, we argue that our model is the appropriate version for
timing games. We show that the notion coincides with the usual one for
discrete-time games. Many timing games in continuous time have only equilibria
in mixed strategies -- in particular preemption games, which often occur in the
strategic real option literature. We provide a sound foundation for some
workhorse equilibria of that literature, which has been lacking as we show. We
obtain a general constructive existence result for subgame-perfect equilibria
in preemption games and illustrate our findings by several explicit
applications.Comment: 27 pages, 1 figur
Subgame-Perfect Equilibria in Stochastic Timing Games
Riedel F, Steg J-H. Subgame-Perfect Equilibria in Stochastic Timing Games. Center for Mathematical Economics Working Papers. Vol 524. Bielefeld: Center for Mathematical Economics; 2014.We introduce a notion of subgames for stochastic timing games and the related
notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of
subgame-perfect equilibrium for continuous-time games is not available in general, we argue
that our model is the appropriate version for timing games. We show that the notion coincides
with the usual one for discrete-time games. Many timing games in continuous time have only
equilibria in mixed strategies – in particular preemption games, which often occur in the
strategic real option literature. We provide a sound foundation for some workhorse equilibria
of that literature, which has been lacking as we show. We obtain a general constructive
existence result for subgame-perfect equilibria in preemption games and illustrate our findings
by several explicit applications
Subgame-perfect equilibria in stochastic timing games
Abstract: We develop a notion of subgames and the related notion of subgame-perfect equilibrium – possibly in mixed strategies – for stochastic timing games. To capture all situations that can arise in continuous-time models, it is necessary to consider stopping times as the starting dates of subgames. We generalize Fudenberg and Tirole’s (1985) mixed-strategy extensions to make them applicable to stochastic timing games and thereby provide a sound basis for subgame-perfect equilibria of preemption games. Sufficient conditions for equilibrium existence are presented, and examples illustrate their application as well as the fact that intuitive arguments can break down in the presence of stochastic processes with jumps
Pure Subgame-Perfect Equilibria in Free Transition Games
We consider a class of stochastic games, where each state is identified with a player. At any moment during play, one of the players is called active. The active player can terminate the game, or he can announce any player, who then becomes the active player. There is a non-negative payoff for each player upon termination of the game, which depends only on the player who decided to terminate. We give a combinatorial proof of the existence of subgame-perfect equilibria in pure strategies for the games in our class.mathematical economics;
Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games
Probabilistic model checking for stochastic games enables formal verification
of systems that comprise competing or collaborating entities operating in a
stochastic environment. Despite good progress in the area, existing approaches
focus on zero-sum goals and cannot reason about scenarios where entities are
endowed with different objectives. In this paper, we propose probabilistic
model checking techniques for concurrent stochastic games based on Nash
equilibria. We extend the temporal logic rPATL (probabilistic alternating-time
temporal logic with rewards) to allow reasoning about players with distinct
quantitative goals, which capture either the probability of an event occurring
or a reward measure. We present algorithms to synthesise strategies that are
subgame perfect social welfare optimal Nash equilibria, i.e., where there is no
incentive for any players to unilaterally change their strategy in any state of
the game, whilst the combined probabilities or rewards are maximised. We
implement our techniques in the PRISM-games tool and apply them to several case
studies, including network protocols and robot navigation, showing the benefits
compared to existing approaches
Dynamic Games with Almost Perfect Information
This paper aims to solve two fundamental problems on finite or infinite
horizon dynamic games with perfect or almost perfect information. Under some
mild conditions, we prove (1) the existence of subgame-perfect equilibria in
general dynamic games with almost perfect information, and (2) the existence of
pure-strategy subgame-perfect equilibria in perfect-information dynamic games
with uncertainty. Our results go beyond previous works on continuous dynamic
games in the sense that public randomization and the continuity requirement on
the state variables are not needed. As an illustrative application, a dynamic
stochastic oligopoly market with intertemporally dependent payoffs is
considered
Extensive-form games and strategic complementarities
I prove the subgame-perfect equivalent of the basic result for Nash equilibria in normal-form games of strategic complements: the set of subgame-perfect equilibria is a nonempty, complete lattice—in particular, subgame-perfect Nash equilibria exist. For this purpose I introduce a device that allows the study of the set of subgame-perfect equilibria as the set of fixed points of a correspondence. My results are limited because extensive-form games of strategic complementarities turn out—surprisingly—to be a very restrictive class of games
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