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New Approaches to Strategic Thinking in Dynamic Games
Mehmet Mars Seven
We present several models of strategic choice concerning equilibrium reasoning and behaviour, as well as new applications to dynamic games. We propose concepts such as historical e…
Correlated optimin
Mehmet Mars Seven
We extend the optimin notion of Ismail (2025) from mixed strategy profiles to correlated distributions. A correlated distribution is evaluated by the worst expected payoff each pla…
Aggregating Elo Ratings: An Axiomatization
Mehmet Mars Seven
Many environments assign several Elo ratings to the same agent: a chess player has classical, rapid, and blitz ratings; an online platform may rate by time control, mode, or format…
How damaging is zero-sum thinking to an agent's interests when the world is positive-sum?
Shaun Hargreaves Heap, Mehmet Mars Seven
We study whether zero-sum decision rules, maximin and minimax, harm agents' interests in positive-sum games relative to Nash equilibrium behaviour or, more generally, than best res…
Performance Rating Equilibrium
Mehmet Mars Seven
In this note, we introduce a novel performance rating system called Performance Rating Equilibrium (PRE). A PRE is a vector of ratings for each player, such that if these ratings w…
Multi-Tier Tournaments: Matching and Scoring Players
Steven J. Brams, Mehmet S. Ismail
We introduce a novel system of matching and scoring players in tournaments, called Multi-Tier Tournaments, illustrated by chess and based on the following rules: 1. Players are div…
Game Intelligence: Theory and Computation
Mehmet Mars Seven
In this paper, I formalize intelligence measurement in games by introducing mechanisms that assign a real number -- interpreted as an intelligence score -- to each player in a game…
Subgame Credible Nash Equilibrium
Mehmet Mars Seven
We propose the Subgame Credible Nash Equilibrium (SCNE), a refinement of subgame perfect Nash equilibrium (SPNE) for multi-stage games. SCNE retains the internal credibility requir…