Identification of Solution Concepts for Discrete Games

2016 ◽  
Author(s):  
Nail Kashaev ◽  
Bruno Salcedo
Keyword(s):  
Solution Concepts ◽  
Discrete Games

Adversarial Risk Analysis for Auctions Using Mirror Equilibrium and Bayes Nash Equilibrium

2021 ◽  
Author(s):  
Muhammad Ejaz ◽  
Stephen Joe ◽  
Chaitanya Joshi
Keyword(s):  
Nash Equilibrium ◽  
Risk Analysis ◽  
Equilibrium Solution ◽  
Risk Averse ◽  
Prior Work ◽  
Reserve Price ◽  
Solution Concepts ◽  
Risk Seeking ◽  
Sealed Bid ◽  
Sealed Bid Auctions

In this paper, we use the adversarial risk analysis (ARA) methodology to model first-price sealed-bid auctions under quite realistic assumptions. We extend prior work to find ARA solutions for mirror equilibrium and Bayes Nash equilibrium solution concepts, not only for risk-neutral but also for risk-averse and risk-seeking bidders. We also consider bidders having different wealth and assume that the auctioned item has a reserve price.

scholarly journals Coalition formation and history dependence

2020 ◽  
Vol 15 (1) ◽  
pp. 159-197 ◽  
Author(s):  
Bhaskar Dutta ◽  
Hannu Vartiainen
Keyword(s):  
Coalition Formation ◽  
Stable Set ◽  
Transferable Utility ◽  
Stable Sets ◽  
Solution Concepts ◽  
History Dependence ◽  
Von Neumann ◽  
Finite Games ◽  
A Chain ◽  
Indirect Dominance

Farsighted formulations of coalitional formation, for instance, by Harsanyi and Ray and Vohra, have typically been based on the von Neumann–Morgenstern stable set. These farsighted stable sets use a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional “moves” in which each coalition that is involved in the sequence eventually stands to gain. Dutta and Vohra point out that these solution concepts do not require coalitions to make optimal moves. Hence, these solution concepts can yield unreasonable predictions. Dutta and Vohra restricted coalitions to hold common, history‐independent expectations that incorporate optimality regarding the continuation path. This paper extends the Dutta–Vohra analysis by allowing for history‐dependent expectations. The paper provides characterization results for two solution concepts that correspond to two versions of optimality. It demonstrates the power of history dependence by establishing nonemptyness results for all finite games as well as transferable utility partition function games. The paper also provides partial comparisons of the solution concepts to other solutions.

scholarly journals Distance-Based Equilibria in Normal-Form Games

2020 ◽  
Vol 34 (02) ◽  
pp. 1750-1757
Author(s):  
Erman Acar ◽  
Reshef Meir
Keyword(s):  
Normal Form ◽  
Behavioral Model ◽  
Existence Results ◽  
Solution Concepts ◽  
Worst Case ◽  
Agent Model ◽  
Normal Form Games ◽  
Strategy Profile ◽  
Action Profile

We propose a simple uncertainty modification for the agent model in normal-form games; at any given strategy profile, the agent can access only a set of “possible profiles” that are within a certain distance from the actual action profile. We investigate the various instantiations in which the agent chooses her strategy using well-known rationales e.g., considering the worst case, or trying to minimize the regret, to cope with such uncertainty. Any such modification in the behavioral model naturally induces a corresponding notion of equilibrium; a distance-based equilibrium. We characterize the relationships between the various equilibria, and also their connections to well-known existing solution concepts such as Trembling-hand perfection. Furthermore, we deliver existence results, and show that for some class of games, such solution concepts can actually lead to better outcomes.

scholarly journals Imposing equilibrium restrictions in the estimation of dynamic discrete games

2021 ◽  
Vol 12 (4) ◽  
pp. 1223-1271 ◽  
Author(s):  
Victor Aguirregabiria ◽  
Mathieu Marcoux
Keyword(s):  
Fixed Point ◽  
Local Convergence ◽  
Asymptotic Properties ◽  
Estimation Algorithms ◽  
Finite Samples ◽  
Spectral Algorithm ◽  
Discrete Games ◽  
Dynamic Discrete Games ◽  
Present Simulation ◽  
Theoretical Results

Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these restrictions have different merits and limitations. Algorithms that guarantee local convergence typically require the approximation of high‐dimensional Jacobians. Alternatively, the Nested Pseudo‐Likelihood (NPL) algorithm is a fixed‐point iterative procedure, which avoids the computation of these matrices, but—in games—may fail to converge to the consistent NPL estimator. In order to better capture the effect of iterating the NPL algorithm in finite samples, we study the asymptotic properties of this algorithm for data generating processes that are in a neighborhood of the NPL fixed‐point stability threshold. We find that there are always samples for which the algorithm fails to converge, and this introduces a selection bias. We also propose a spectral algorithm to compute the NPL estimator. This algorithm satisfies local convergence and avoids the approximation of Jacobian matrices. We present simulation evidence and an empirical application illustrating our theoretical results and the good properties of the spectral algorithm.

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