Solution Concepts for Games with General Coalitional Structure

2011 ◽  
Author(s):  
Gleb A. Koshevoy ◽  
Dolf J. J. Talman
Keyword(s):  
Solution Concepts ◽  
Coalitional Structure

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 Are Category Labels Primary? Children Use Similarities to Reason About Social Groups

2020 ◽  
Author(s):  
Ashley Jordan ◽  
Yarrow Dunham
Keyword(s):  
Young Children ◽  
Social Groups ◽  
Structure Study ◽  
Group Representations ◽  
Common Assumption ◽  
Low Level ◽  
Coalitional Structure ◽  
Category Labels ◽  
Types Of Information ◽  
Social Inferences

While interpersonal similarities impact young children’s peer judgments, little work has assessed whether they also guide group-based reasoning. A common assumption has been that category labels rather than “mere” similarities are unique constituents of such reasoning; the present work challenges this. Children (ages 3–9) viewed groups defined by category labels or shared preferences, and their social inferences were assessed. By age 5, children used both types of information to license predictions about preferences (Study 1, n = 129) and richer forms of coalitional structure (Study 2, n = 205). Low-level explanations could not account for this pattern (Study 3, n = 72). Finally, older but not younger children privileged labeled categories when they were pitted against similarity (Study 4, n = 51). These studies show that young children use shared preferences to reason about relationships and coalitional structure, suggesting that similarities are central to the emergence of group representations.

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.

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