Related papers: Hydra games for recursively Mahlo operations
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The recursive path ordering is an established and crucial tool in term rewriting to prove termination. We revisit its presentation by means of some simple rules on trees (or corresponding terms) equipped with a 'star' as control symbol,…
In this paper we address a problem: How far can we iterate lower recursively Mahlo operations in higher reflecting universes? Or formally: How much can lower recursively Mahlo operations be iterated in set theories for higher reflecting…
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Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players'…
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In this note we axiomatize the $\Pi_{k+1}$-consequences in the set theory ${\sf KP}\Pi_{N}$ for $\Pi_{N}$-reflecting universes in terms of iterations of $\Pi_{i}$-recursively Mahlo operations for $1\leq k\leq i<N$.
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A partial differential equation is derived, describing the replicator dynamics with mutations of games with a continuous strategy space. This equation is then applied to continuous versions of symmetric 2x2 games, such as the Prisoners…
Compositional Game Theory is a new, recently introduced model of economic games based upon the computer science idea of compositionality. In it, complex and irregular games can be built up from smaller and simpler games, and the equilibria…
To predict the behavior of a population game when time becomes very long, the process that characterizes the evolution of our game dynamics must be reversible. Known games satisfying this are 2 strategy games as well as potential games with…
The Sato-Crutchfield equations are studied analytically and numerically. The Sato-Crutchfield formulation is corresponding to losing memory. Then Sato-Crutchfield formulation is applied for some different types of games including hawk-dove,…
The present work consisted in developing a plateau game. There are the traditional ones (monopoly, cluedo, ect.) but those which interest us leave less place at the chance (luck) than to the strategy such that the chess game. Kallah is an…
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Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games…
The Collatz dynamic is known to generate a complex quiver of sequences over natural numbers which inflation propensity remains so unpredictable it could be used to generate reliable proof of work algorithms for the cryptocurrency industry.…
The set theory KP$\Pi_{N+1}$ for $\Pi_{N+1}$-reflecting universes is shown to be $\Pi_{N+1}$-conservative over iterations of $\Pi_{N}$-recursively Mahlo operations for each $N\geq 2$.