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Which Is the Worst-Case Nash Equilibrium? [chapter]

Thomas Lücking, Marios Mavronicolas, Burkhard Monien, Manuel Rode, Paul Spirakis, Imrich Vrto
2003 Lecture Notes in Computer Science  
, is the worst-case Nash equilibrium.  ...  In particular, we are interested in identifying the worst-case Nash equilibrium -the one that maximizes social cost.  ...  The worst-case Nash equilibrium is one that maximizes social cost.  ... 
doi:10.1007/978-3-540-45138-9_49 fatcat:now2k3qnmfazjodfrkmscgxz7i

Safe Equilibrium [article]

Sam Ganzfried
2022 arXiv   pre-print
On the other hand, a maximin strategy assumes that all opposing agents are playing to minimize our payoff (even if it is not in their best interest), and ensures the maximal possible worst-case payoff,  ...  The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally.  ...  realistic than the worst-case assumption.  ... 
arXiv:2201.04266v5 fatcat:rc7d2esn5fex5idihxycnjdysy

Beyond equilibrium

James Wright
2010 Proceedings of the Behavioral and Quantitative Game Theory on Conference on Future Directions - BQGT '10  
It is standard in multiagent settings to assume that agents will adopt Nash equilibrium strategies.  ...  However, studies in experimental economics demonstrate that Nash equilibrium is a poor description of human players' actual behaviour.  ...  First and foremost, I would like to thank my supervisor Kevin Leyton-Brown, for introducing me to behavioural game theory in the first place, and for his continued guidance in every aspect of research.  ... 
doi:10.1145/1807406.1807449 dblp:conf/bqgt/Wright10 fatcat:ua23q7lrijelbabnb5csq462nm

Conditional strategy equilibrium [article]

Lorenzo Bastianello, Mehmet S. Ismail
2022 arXiv   pre-print
In this note, we prove the existence of an equilibrium concept, dubbed conditional strategy equilibrium, for non-cooperative games in which a strategy of a player is a function from the other players'  ...  We study the properties of efficiency and coalition-proofness of the conditional strategy equilibrium in n-person games.  ...  benchmark model, we assume that a conditional strategy profile that produces a disagreement induces the worst utility in the game to the players, which is similar to the disagreement outcome in the Nash  ... 
arXiv:2103.06928v3 fatcat:oawkkok5mrdalasud5qlsp4rpm

Legitimate equilibrium

János Flesch, Dries Vermeulen, Anna Zseleva
2021 International Journal of Game Theory  
AbstractWe present a general existence result for a type of equilibrium in normal-form games, which extends the concept of Nash equilibrium.  ...  A strategy profile is called a legitimate equilibrium if each player evaluates this profile by the upper integral, and each player evaluates all his possible deviations by the lower integral.  ...  This new equilibrium concept is a novel generalisation of the concept of Nash equilibrium.  ... 
doi:10.1007/s00182-021-00768-y fatcat:grnewjeybnda3ae3ufcc5qh37e

Empirical Equilibrium [article]

Rodrigo A. Velez, Alexander L. Brown
2020 arXiv   pre-print
We study the foundations of empirical equilibrium, a refinement of Nash equilibrium that is based on a non-parametric characterization of empirical distributions of behavior in games (Velez and Brown,2020b  ...  The refinement can be alternatively defined as those Nash equilibria that do not refute the regular QRE theory of Goeree, Holt, and Palfrey (2005).  ...  If some of these outcomes are implausible, then a worst case scenario analysis can be unnecessarily pessimistic, and a best case scenario analysis can be unrealistically optimistic.  ... 
arXiv:1804.07986v3 fatcat:jycmtwma2nfijf7kj57mtnlaau

Cursed Equilibrium

Erik Eyster, Matthew Rabin
2005 Econometrica  
sets better than the parameter value corresponding to Bayesian Nash equilibrium.  ...  We test a single-parameter variant of our model that embeds Bayesian Nash equilibrium as a special case and find that parameter values corresponding to cursedness fit a broad range of experimental data  ...  Moreover, the existence of a Bayesian Nash equilibrium (which is to say, a χ = 0 cursed equilibrium) is neither necessary nor sufficient for the existence of a χ-cursed equilibrium for each χ ∈ (0, 1].  ... 
doi:10.1111/j.1468-0262.2005.00631.x fatcat:icg67v54ejgwrmifpqr2disr6y

Stackelberg versus Cournot Equilibrium

Rabah Amir, Isabel Grilo
1999 Games and Economic Behavior  
While our findings essentially confirm the predominance of the former, they also indicate that the latter is natural under some robust but restrictive conditions.  ...  For quantity duopoly we provide different sets of minimal conditions, directly on the demand and cost functions, yielding respectively the simultaneous and the two sequential modes of play.  ...  2 y > y s P x s + y s − C 2 y s This says that the follower prefers the worst Cournot-Nash equilibrium (for himself) to any Stackelberg equilibrium.  ... 
doi:10.1006/game.1998.0650 fatcat:ioie6d6rq5chvcfgknsxw5dqai

How long to equilibrium? The communication complexity of uncoupled equilibrium procedures

Sergiu Hart, Yishay Mansour
2010 Games and Economic Behavior  
Specifically, we show lower bounds that are exponential in the number of players in each one of the following cases: (1) reaching a pure Nash equilibrium; (2) reaching a pure Nash equilibrium in a Bayesian  ...  We then show that, in contrast, the communication complexity of reaching a correlated equilibrium is polynomial in the number of players.  ...  The research was partially supported by grants of the Israel Science Foundation (Hart, Mansour) and by an IBM faculty award (Mansour).  ... 
doi:10.1016/j.geb.2007.12.002 fatcat:xeqrst7hazbyrg6islro2m5epm


Sergiu Hart, Yishay Mansour
2013 World Scientific Series in Economic Theory  
Specifically, we show lower bounds that are exponential in the number of players in each one of the following cases: (1) reaching a pure Nash equilibrium; (2) reaching a pure Nash equilibrium in a Bayesian  ...  We then show that, in contrast, the communication complexity of reaching a correlated equilibrium is polynomial in the number of players.  ...  The research was partially supported by grants of the Israel Science Foundation (Hart, Mansour) and by an IBM faculty award (Mansour).  ... 
doi:10.1142/9789814390705_0010 fatcat:pvappj4jpbgz7pfd3ukqfa5g5i

Perfect Prediction Equilibrium [article]

Ghislain Fourny and Stéphane Reiche and Jean-Pierre Dupuy
2015 arXiv   pre-print
Finally, the PPE is put in perspective with existing literature (Newcomb's Problem, Superrationality, Nash Equilibrium, Subgame Perfect Equilibrium, Backward Induction Paradox, Forward Induction).  ...  In the Nash paradigm, rational players consider that the opponent's strategy is fixed while maximizing their payoff.  ...  Introduction In non-cooperative game theory, one of the most common equilibrium concepts is the Subgame Perfect Equilibrium (SPE) (Selten 1965) , a refinement of the Nash Equilibrium (Nash 1951) .  ... 
arXiv:1409.6172v2 fatcat:j7mq5xe5yzhphpwvk6ehaq5ave

Learning and Equilibrium

Drew Fudenberg, David K. Levine
2009 Annual Review of Economics  
If agents' strategies are completely observed at the end of each round, and agents are randomly matched with a series of anonymous opponents, fairly simple rules perform well in terms of the agent's worst-case  ...  The theory of learning in games studies how, which and what kind of equilibria might arise as a consequence of a long-run non-equilibrium process of learning, adaptation and/or imitation.  ...  This universality property (called worst-case analysis in computer science) has proven important in the theory of learning, perhaps because it is fairly easy to achieve.  ... 
doi:10.1146/annurev.economics.050708.142930 fatcat:tpech5epxffvfhvm2cy5vk66u4

Equilibrium in Combinatorial Public Projects [chapter]

Brendan Lucier, Yaron Singer, Vasilis Syrgkanis, Éva Tardos
2013 Lecture Notes in Computer Science  
For Pure Nash Equilibria we show that the worst-case loss in efficiency is proportional to the number of agents.  ...  For public projects in which only one item is selected we show constructively that there always exists a Pure Nash Equilibrium that guarantees at least 1 2 (1 − 1 n ) of the optimum.  ...  For each equilibrium notion above, we can measure worst-case efficiency by way of the price of anarchy.  ... 
doi:10.1007/978-3-642-45046-4_28 fatcat:5h6d6hnmkjbnxhyeo6ah4mbu2q

Team-maxmin equilibrium: efficiency bounds and algorithms [article]

Nicola Basilico, Andrea Celli, Giuseppe De Nittis, Nicola Gatti
2016 arXiv   pre-print
In this paper, we investigate bounds of (in)efficiency of the Team-maxmin equilibrium w.r.t. the Nash equilibria and w.r.t. the Maxmin equilibrium when the team members can play correlated strategies.  ...  Nevertheless, to the best of our knowledge, the Team-maxmin equilibrium is almost completely unexplored in the literature.  ...  Therefore, there are instances in which the worst Nash equilibrium is arbitrarily worse than the Team-maxmin equilibrium and, in its turn, the Team-maxmin equilibrium is arbitrarily worse (in this case  ... 
arXiv:1611.06134v1 fatcat:fjolrrvx2rhdzniyc5zlch4meq

Collusion constrained equilibrium

Rohan Dutta, David K. Levine, Salvatore Modica
2018 Theoretical Economics  
In each case we show that equilibria in which groups choose the best alternative exist and that limits of these equilibria lead to collusion constrained equilibria.  ...  This allows groups to randomize between alternatives to which they are not indifferent in certain razor's edge cases where slight perturbations of group beliefs change the set of incentive compatible plans  ...  ADEMU is funded by the European Union's Horizon 2020 Program under grant agreement N° 649396 (ADEMU). _________________________ The ADEMU Working Paper Series is being supported by the European Commission  ... 
doi:10.3982/te2762 fatcat:7zkptp6fhjdx5drokbdtgs7the
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