ترغب بنشر مسار تعليمي؟ اضغط هنا

Extensive Infinite Games and Escalation, an exercise in Agda

78   0   0.0 ( 0 )
 نشر من قبل Pierre Lescanne
 تاريخ النشر 2020
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English
 تأليف Pierre Lescanne




اسأل ChatGPT حول البحث

Escalation in games is when agents keep playing forever. Based on formal proofs we claim that if agents assume that resource are infinite, escalation is rational.



قيم البحث

اقرأ أيضاً

151 - Pierre Lescanne 2016
Extensive games are tools largely used in economics to describe decision processes ofa community of agents. In this paper we propose a formal presentation based on theproof assistant COQ which focuses mostly on infinite extensive games and theirchara cteristics. COQ proposes a feature called dependent types, which meansthat the type of an object may depend on the type of its components. For instance,the set of choices or the set of utilities of an agent may depend on the agentherself. Using dependent types, we describe formally a very general class of gamesand strategy profiles, which corresponds somewhat to what game theorists are used to.We also discuss the notions of infiniteness in game theory and how this can beprecisely described.
108 - Olivier Finkel 2008
Omega-powers of finitary languages are omega languages in the form V^omega, where V is a finitary language over a finite alphabet X. Since the set of infinite words over X can be equipped with the usual Cantor topology, the question of the topologica l complexity of omega-powers naturally arises and has been raised by Niwinski, by Simonnet, and by Staiger. It has been recently proved that for each integer n > 0, there exist some omega-powers of context free languages which are Pi^0_n-complete Borel sets, and that there exists a context free language L such that L^omega is analytic but not Borel. But the question was still open whether there exists a finitary language V such that V^omega is a Borel set of infinite rank. We answer this question in this paper, giving an example of a finitary language whose omega-power is Borel of infinite rank.
154 - Olivier Finkel 2008
We consider the set of infinite real traces, over a dependence alphabet (Gamma, D) with no isolated letter, equipped with the topology induced by the prefix metric. We then prove that all rational languages of infinite real traces are analytic sets a nd that there exist some rational languages of infinite real traces which are analytic but non Borel sets, and even Sigma^1_1-complete, hence of maximum possible topological complexity.
113 - Olivier Finkel 2013
We prove that the determinacy of Gale-Stewart games whose winning sets are infinitary rational relations accepted by 2-tape Buchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardin al assumption. Then we prove that winning strategies, when they exist, can be very complex, i.e. highly non-effective, in these games. We prove the same results for Gale-Stewart games with winning sets accepted by real-time 1-counter Buchi automata, then extending previous results obtained about these games. Then we consider the strenghs of determinacy for these games, and we prove that there is a transfinite sequence of 2-tape Buchi automata (respectively, of real-time 1-counter Buchi automata) $A_alpha$, indexed by recursive ordinals, such that the games $G(L(A_alpha))$ have strictly increasing strenghs of determinacy. Moreover there is a 2-tape Buchi automaton (respectively, a real-time 1-counter Buchi automaton) B such that the determinacy of G(L(B)) is equivalent to the (effective) analytic determinacy and thus has the maximal strength of determinacy. We show also that the determinacy of Wadge games between two players in charge of infinitary rational relations accepted by 2-tape Buchi automata is equivalent to the (effective) analytic determinacy, and thus not provable in ZFC.
In this paper we investigate the $lambda$ -calculus, a $lambda$-calculus enriched with resource control. Explicit control of resources is enabled by the presence of erasure and duplication operators, which correspond to thinning and con-traction rule s in the type assignment system. We introduce directly the class of $lambda$ -terms and we provide a new treatment of substitution by its decompo-sition into atomic steps. We propose an intersection type assignment system for $lambda$ -calculus which makes a clear correspondence between three roles of variables and three kinds of intersection types. Finally, we provide the characterisation of strong normalisation in $lambda$ -calculus by means of an in-tersection type assignment system. This process uses typeability of normal forms, redex subject expansion and reducibility method.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا