Related papers: Deduction Theorem: The Problematic Nature of Commo…
The increasingly pervasive connectivity of today's information systems brings up new challenges to security. Traditional security has accomplished a long way toward protecting well-defined goals such as confidentiality, integrity,…
Bayesian networks and their accompanying graphical models are widely used for prediction and analysis across many disciplines. We will reformulate these in terms of linear maps. This reformulation will suggest a natural extension, which we…
Defeasible reasoning is a kind of reasoning where some generalisations may not be valid in all circumstances, that is general conclusions may fail in some cases. Various formalisms have been developed to model this kind of reasoning, which…
We introduce a pebble game extended by backtracking options for one of the two players (called Prover) and reduce the provability of the pigeonhole principle for a generic predicate $R$ in the bounded arithmetic $T^2_2(R)$ to the existence…
The field of Game Theory provides a useful mechanism for modeling many decision-making scenarios. In participating in these scenarios individuals and groups adopt particular strategies, which generally perform with varying levels of…
The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace…
In repeated-game applications where both the collusive and non-collusive outcomes can be supported as equilibria, researchers must resolve underlying selection questions if theory will be used to understand counterfactual policies. One…
Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…
Temperature of combinatorial games have been long studied since when Conway established the modern combinatorial game theory, and there are several variations of the concepts. In this article, we focus on one of the classical versions of…
Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning…
Fictitious play is a simple and widely studied adaptive heuristic for playing repeated games. It is well known that fictitious play fails to be Hannan consistent. Several variants of fictitious play including regret matching, generalized…
We consider a family of distributions on which natural tail orders can be constructed upon a representation of a distribution by a (single) hyper-real number. Past research revealed that the ordering can herein strongly depend on the…
Game-playing proofs constitute a powerful framework for non-quantum cryptographic security arguments, most notably applied in the context of indifferentiability. An essential ingredient in such proofs is lazy sampling of random primitives.…
We propose a unifying additive theory for standard conventions in Combinatorial Game Theory, including normal-, mis\`ere- and scoring-play, studied by Berlekamp, Conway, Dorbec, Ettinger, Guy, Larsson, Milley, Neto, Nowakowski, Renault,…
A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all real-world players. A recurring issue in statistical physics is how best to approximate joint probability…
The famous G\"odel incompleteness theorem says that for every sufficiently rich formal theory (containing formal arithmetic in some natural sense) there exist true unprovable statements. Such statements would be natural candidates for being…
We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.
This note makes the obvious observation that Hoeffding's original proof of his inequality remains valid in the game-theoretic framework. All details are spelled out for the convenience of future reference.
Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…
In many expert and everyday reasoning contexts it is very useful to reason on the basis of defeasible assumptions. For instance, if the information at hand is incomplete we often use plausible assumptions, or if the information is…