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The approach shows that several classical results, including existence of Nash equilibrium, can fail once computational costs affect utilities. The framework also explains observed behavior in well-studied games and provides conditions that still guarantee equilibrium existence. As an application, the paper defines protocol security via game-theoretic implementation notions and links it to a variant of traditional cryptographic simulation-based security.",{"@graph":69,"@context":127},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/game-theory-with-costly-computation-formulation-and-application-to-protocol-security/148674/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/game-theory-with-costly-computation-formulation-and-application-to-protocol-security/148674.png","ImageObject",300,407,{"name":92,"@type":93},"Fahsai","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","2026-08-26",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119,123],{"name":110,"@type":111,"acceptedAnswer":112},"What problem does the paper address?","Question",{"text":113,"@type":114},"It studies strategic interaction when agents’ computation can be costly, so computational effort directly impacts their utilities and equilibrium reasoning.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does costly computation change standard game-theoretic conclusions?",{"text":118,"@type":114},"Many classical results, such as guaranteed existence of Nash equilibrium, may no longer hold when computation costs are taken into account.",{"name":120,"@type":111,"acceptedAnswer":121},"What conditions does the paper provide?",{"text":122,"@type":114},"It derives natural conditions on games under which equilibria are guaranteed to exist, even in the presence of costly computation.",{"name":124,"@type":111,"acceptedAnswer":125},"How is protocol security connected to the game-theoretic framework?",{"text":126,"@type":114},"The paper defines protocol security using game-theoretic notions of implementation and shows a special case equivalent to a simulation-based variant of the traditional cryptographic definition.","https://schema.org",{"og:url":83,"og:type":129,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":131,"canonical":83},"index,follow",{"doc_id":133,"site_id":62},148674,1787782933,{"code":4,"msg":5,"data":136},{"doc_id":133,"user_id":137,"nickname":92,"user_avatar":138,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":139,"file_id":140,"file_url":141,"file_type":142,"file_size":143,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":144,"language":145,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":146,"faqs":147,"seo_title":148,"seo_description":67,"update_tm":134,"read_time":149,"preview_page_count":4},549768702563,"https://ap-avatar.wpscdn.com/avatar/8000c4aa63b76e948b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786536092046926083","Game Theory with Costly Computation: Formulation and Application to Protocol Security  \nJoseph Y. Halpern􀀃 Rafael Passy  \nCornell University  \n[halpern@cs.cornell.edu](halpern@cs.cornell.edu) [rafael@cs.cornell.edu](rafael@cs.cornell.edu)  \nAbstract: We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer hold. Nevertheless, we can use the framework to provide psychologically appealing explanations to observed behavior in well-studied games (such as finitely repeated prisoner's dilemma and rock-paper-scissors) . Furthermore, we provide natural conditions on games sufficient to guarantee that equilibria exist. As an application of this framework, we develop a definition of protocol security relying on game-theoretic notions of implementation. We show that a natural special case of this this definition is equivalent to a variant of the traditional cryptographic definition of protocol security; this result shows that, when taking computation into account, the two approaches used for dealing with “deviating” players in two different communities—Nash equilibrium in game theory and zero-knowledge“simulation” in cryptography—are intimately related.  \nKeywords: game theory, costly computation, cryptography  \n1 Introduction  \nConsider the following game. You are given a random odd n-bit number x and you are supposed to decide whether x is prime or composite. If you guess correctly you receive $2, if you guess incorrectly you instead have to pay a penalty of $1000 . Additionally you have the choice of “playing safe” by giving up, in which case you receive $1 . In traditional game theory, computation is considered “costless”; in other words, players are allowed to perform an unbounded amount of computation without it affecting their utility. Traditional game theory suggests that you should compute whether x is prime or composite and output the correct answer; this is the only Nash equilibrium of the one-person game, no matter what n (the size of the prime) is. Although for small n this seems reasonable, when n grows larger most people would probably decide to “play safe”—as eventually the cost of computing the answer (e.g., by buying powerful enough computers) outweighs the possible gain of $1 .  \nThe importance of considering such computational issues in game theory has been recognized since at least the work of Simon [1] . There have been a number of attempts to capture various aspects of computation. Two major lines of research can be identified. The first line, initiated by Neyman [2], tries to model the fact that play-  \n􀀃 Supported in part by NSF grants ITR-0325453, IIS-0534064, IIS- 0812045, and IIS-0911036, and by AFOSR grants FA9550-08-1-0438 and FA9550-09-1-0266, and ARO grant W911NF-09-1-0281 .  \ny Supported in part by a Microsoft New Faculty Fellowship, NSF CAREER Award CCF-0746990, AFOSR Award FA9550-08-1-0197, and BSF Grant 2006317 .  \ners can do only bounded computation, typically by modeling players as finite automata. Neyman focused on finitely repeated prisoner's dilemma, a topic which has contined to attract attention. (See [3] and the references therein for more recent work on prisoner's dilemma played by finite automata; Megiddo and Wigderson [4] considered prisoner's dilemma played by Turing machines.) In another instance of this line of research, Dodis, Halevi, and Rabin [5] and Urbano and Vila [6] consider the problem of implementing mediators when players are polynomial-time Turing machines. The second line, initiated by Rubinstein [7], tries to capture the fact that doing costly computation affects an agent's utility. Rubinstein assumed that players choose a finite automaton to play the game rather than choosing a strategy directly; a player's utility depends both on the move made by the automaton and the complexity of the automaton (identified ","cbCaiafq1ety0P7q","https://ap.wps.com/l/cbCaiafq1ety0P7q","pdf",350388,21,"English","# Introduction\n## Background: Traditional vs. Costly Computation in Game Theory\n## Two Research Lines on Modeling Computation\n## Proposed Framework and Key Modeling Choices\n## Equilibrium and Other Classical Results under Costly Computation\n## Application: Game-Theoretic Protocol Security","[{\"question\":\"What problem does the paper address?\",\"answer\":\"It studies strategic interaction when agents’ computation can be costly, so computational effort directly impacts their utilities and equilibrium reasoning.\"},{\"question\":\"How does costly computation change standard game-theoretic conclusions?\",\"answer\":\"Many classical results, such as guaranteed existence of Nash equilibrium, may no longer hold when computation costs are taken into account.\"},{\"question\":\"What conditions does the paper provide?\",\"answer\":\"It derives natural conditions on games under which equilibria are guaranteed to exist, even in the presence of costly computation.\"},{\"question\":\"How is protocol security connected to the game-theoretic framework?\",\"answer\":\"The paper defines protocol security using game-theoretic notions of implementation and shows a special case equivalent to a simulation-based variant of the traditional cryptographic definition.\"}]","Game Theory with Costly Computation - Formulation and Application to Protocol Security | PDF",53]