45 research outputs found
How Discontinuous is Computing Nash Equilibria? (Extended Abstract)
We investigate the degree of discontinuity of several solution concepts from non-cooperative game theory. While the consideration of Nash equilibria forms the core of our work, also pure and correlated equilibria are dealt with. Formally, we restrict the treatment to two player games, but results and proofs extend to the -player case. As a side result, the degree of discontinuity of solving systems of linear inequalities is settled
Abstracting Imperfect Information Away from Two-Player Zero-Sum Games
In their seminal work, Nayyar et al. (2013) showed that imperfect information
can be abstracted away from common-payoff games by having players publicly
announce their policies as they play. This insight underpins sound solvers and
decision-time planning algorithms for common-payoff games. Unfortunately, a
naive application of the same insight to two-player zero-sum games fails
because Nash equilibria of the game with public policy announcements may not
correspond to Nash equilibria of the original game. As a consequence, existing
sound decision-time planning algorithms require complicated additional
mechanisms that have unappealing properties. The main contribution of this work
is showing that certain regularized equilibria do not possess the
aforementioned non-correspondence problem -- thus, computing them can be
treated as perfect information problems. Because these regularized equilibria
can be made arbitrarily close to Nash equilibria, our result opens the door to
a new perspective on solving two-player zero-sum games and, in particular,
yields a simplified framework for decision-time planning in two-player zero-sum
games, void of the unappealing properties that plague existing decision-time
planning approaches
A Game of Competition for Risk
In this study, we present models where participants strategically select
their risk levels and earn corresponding rewards, mirroring real-world
competition across various sectors. Our analysis starts with a normal form game
involving two players in a continuous action space, confirming the existence
and uniqueness of a Nash equilibrium and providing an analytical solution. We
then extend this analysis to multi-player scenarios, introducing a new
numerical algorithm for its calculation. A key novelty of our work lies in
using regret minimization algorithms to solve continuous games through
discretization. This groundbreaking approach enables us to incorporate
additional real-world factors like market frictions and risk correlations among
firms. We also experimentally validate that the Nash equilibrium in our model
also serves as a correlated equilibrium. Our findings illuminate how market
frictions and risk correlations affect strategic risk-taking. We also explore
how policy measures can impact risk-taking and its associated rewards, with our
model providing broader applicability than the Diamond-Dybvig framework. We
make our methodology and open-source code available at
https://github.com/louisabraham/cfrgame
Finally, we contribute methodologically by advocating the use of algorithms
in economics, shifting focus from finite games to games with continuous action
sets. Our study provides a solid framework for analyzing strategic interactions
in continuous action games, emphasizing the importance of market frictions,
risk correlations, and policy measures in strategic risk-taking dynamics
Common Agency and Computational Complexity: Theory and Experimental Evidence
In a common agency game, several principals try to influence the behavior of an agent. Common agency games typically have multiple equilibria. One class of equilibria, called truthful, has been identified by Bernheim and Whinston and has found widespread use in the political economy literature. In this paper we identify another class of equilibria, which we call natural. In a natural equilibrium, each principal offers a strictly positive contribution on at most one alternative. We show that a natural equilibrium always exists and that its computational complexity is much smaller than that of a truthful equilibrium. To compare the predictive power of the two concepts, we run an experiment on a common agency game for which the two equilibria predict a different equilibrium alternative. The results strongly reject the truthful equilibrium. The alternative predicted by the natural equilibrium is chosen in 65% of the matches, while the one predicted by the truthful equilibrium is chosen in less than 5% of the matches.lobbying;experimental economics;common agency;truthful equilibrium;natural equilibrium;computational complexity
How Incomputable is Finding Nash Equilibria?
We investigate the Weihrauch-degree of several solution concepts from noncooperative game theory. While the consideration of Nash equilibria forms the core of our work, also pure and correlated equilibria, as well as various concepts of iterated strategy elimination, are dealt with. As a side result, the Weihrauch-degree of solving systems of linear inequalities is settled