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Repeated Matching Pennies with Limited Randomness [article]

Michele Budinich, Lance Fortnow
2011 arXiv   pre-print
We consider a repeated Matching Pennies game in which players have limited access to randomness. Playing the (unique) Nash equilibrium in this n-stage game requires n random bits.  ...  When the game is played for an infinite amount of rounds with time discounted utilities, under reasonable assumptions, we can reduce the amount of randomness required to achieve a e-Nash equilibrium to  ...  Specifically, we consider the repeated version of Matching Pennies, played for n rounds.  ... 
arXiv:1102.1096v2 fatcat:y7e4vr7icjbi3cajasnnc43jzy

Repeated matching pennies with limited randomness

Michele Budinich, Lance Fortnow
2011 Proceedings of the 12th ACM conference on Electronic commerce - EC '11  
We consider a repeated Matching Pennies game in which players have limited access to randomness. Playing the (unique) Nash equilibrium in this n-stage game requires n random bits.  ...  Can there be Nash equilibria (or ε-Nash equilibria) that use less than n random coins?  ...  Specifically, we consider the repeated version of Matching Pennies, played for n rounds.  ... 
doi:10.1145/1993574.1993592 dblp:conf/sigecom/BudinichF11 fatcat:rwdz3hmycnf47luxucfb3lonzi

When Can Limited Randomness Be Used in Repeated Games?

Pavel Hubáček, Moni Naor, Jonathan Ullman
2016 Theory of Computing Systems  
In this work, we ask whether randomness is necessary for equilibria to exist in finitely repeated games.  ...  We show that, in contrast, in repeated two-player zero-sum games, if pseudorandom generators do not exist, then Ω(n) random bits remain necessary for equilibria to exist.  ...  Specifically, they looked at the "repeated matching pennies."  ... 
doi:10.1007/s00224-016-9690-4 fatcat:qtnezgsljvgljgi6c5zww7fgke

Learning to Be Unpredictable: An Experimental Study

Arijit Mukherji, David E. Runkle
2000 Quarterly Review  
Three-Person Matching Pennies The use of sophisticated Bayesian learning can be tested, however, with a three-person matching pennies game.  ...  limited information play the mixed-strategy Nash equilibrium if subjects with complete information do not?  ... 
doi:10.21034/qr.2422 fatcat:4yrslnls3na2vcmcbzanivvgcq

When Can Limited Randomness Be Used in Repeated Games? [article]

Pavel Hubáček, Moni Naor, Jonathan Ullman
2015 arXiv   pre-print
In this work, we ask whether randomness is necessary for equilibria to exist in finitely repeated games.  ...  We show that, in contrast, in repeated two-player zero-sum games, if pseudorandom generators do not exist, then Ω(n) random bits remain necessary for equilibria to exist.  ...  Specifically, they looked at the "repeated matching pennies."  ... 
arXiv:1507.01191v1 fatcat:ntz7qymgwzbt3bizppm5k6hckq

Random Actions in Experimental Zero-Sum Games

Jung S. You
2021 Journal of Economics and Behavioral Studies  
My results confirm that most players behave differently from the Nash equilibrium prediction for the simplest 2x2 zero-sum game (matching-pennies) and 3x3 zero-sum game (e.g., the rock-paper-scissors game  ...  Playing mixed strategies, however, poses a challenge, as the game theory involves calculating probabilities and executing random actions.  ...  The matching-pennies game has a unique equilibrium: both players randomize with probabilities .5 and .5, respectively.  ... 
doi:10.22610/jebs.v13i1(j).3150 fatcat:y5ypt3nnyfcmlhyocqep4b2mye

Edgar Allan Poe's riddle: Framing effects in repeated matching pennies games

Kfir Eliaz, Ariel Rubinstein
2011 Games and Economic Behavior  
Framing effects have a significant influence on the finitely repeated matching pennies game.  ...  The combination of being labelled "a guesser", and having the objective of matching the opponent's action, appears to be advantageous.  ...  Consider a repeated matching-pennies game, where it is player 2 who wins a stage game if the choices match. Each player chooses his initial action at random.  ... 
doi:10.1016/j.geb.2009.05.010 fatcat:dasxzszynbf4pejk7ugw7ze77u

Evolutionary matching-pennies game on bipartite regular networks

György Szabó, Levente Varga, István Borsos
2014 Physical Review E  
Each player's income comes from matching-pennies games played with the four neighbors.  ...  Evolutionary games are studied here with two types of players located on a chessboard or on a bipartite random regular graph.  ...  of matching-pennies games.  ... 
doi:10.1103/physreve.89.042820 pmid:24827306 fatcat:otsngtqqnrbcbdghqjdu3qnxim

On Hagelbarger's and Shannon's matching pennies playing machines

Macarie Breazu, Daniel Volovici, Daniel I. Morariu, Radu G. Crețulescu
2020 International Journal of Advanced Statistics and IT&C for Economics and Life Sciences  
AbstractIn the 1950s, Hagelbarger's Sequence Extrapolating Robot (SEER) and Shannon's Mind-Reading Machine (MRM) were the state-of-the-art research results in playing the well-known "matching pennies"  ...  Also, we propose a simple contextual predictor (SCP) and use it to compete with SEER and MRM.  ...  In the 1950', at Bell Laboratories, David Hagelbarger and Claude Shannon each build their own machines to play the matching pennies game with lab colleagues (Claude Shannon built also other interesting  ... 
doi:10.2478/ijasitels-2020-0003 fatcat:fyck72trdzc3llmfblfx6iycrm

Generating Ambiguity in the Laboratory

Jack Stecher, Timothy Shields, John Dickhaut
2011 Management science  
The method provides researchers with a way to give subjects the experience of ambiguity.  ...  This matches our procedure with pseudo-random numbers. After generating a sequence of 30 observations in this way, we mapped the results to the interval {1, . . . , 10}.  ...  As finite means and variances underlie laws of large numbers and central limit theorems, it is unsurprising that neither holds for a Cauchy random variable.  ... 
doi:10.1287/mnsc.1100.1307 fatcat:hpqvevcaefepjhf3kl3yerelqq

Estimating the Use of Higher-Order Theory of Mind Using Computational Agents

Harmen de Weerd, Denny Diepgrond, Rineke Verbrugge
2018 The B.E. Journal of Theoretical Economics  
pennies.  ...  This may indicate that human reasoners do not primarily use their theory of mind abilities to compete with others.  ...  repeated versions of matching pennies in two different empirical studies.  ... 
doi:10.1515/bejte-2016-0184 fatcat:fmei4h5qxjg4hp75al7cynolam

How to play with a biased coin?

Olivier Gossner, Nicolas Vieille
2002 Games and Economic Behavior  
We characterize the max min of repeated zero-sum games in which player one plays in pure strategies conditional on the private observation of a fixed sequence of random variables.  ...  The repeated game G ∞ proceeds as follows. We let X = (X n ) n 1 be a sequence of i.i.d., random variables, each with law p, with values in a finite set C.  ...  To guarantee: matching pennies We construct an ε-optimal strategy for player one in the game of matching pennies, assuming C = {0, 1}.  ... 
doi:10.1016/s0899-8256(02)00507-9 fatcat:u5bnexgewfcglhz4zvnblvn4pi

The Anterior Insula Tracks Behavioral Entropy during an Interpersonal Competitive Game

Hideyuki Takahashi, Keise Izuma, Madoka Matsumoto, Kenji Matsumoto, Takashi Omori, Katsumi Watanabe
2015 PLoS ONE  
While undergoing functional magnetic resonance imaging (fMRI), subjects played matching pennies with either a human or computer opponent in each block, although in reality they played the game with the  ...  In the present study, we investigated the neural basis of how individuals adjust their strategy during a simple, competitive game of matching pennies.  ...  situation, such as a matching pennies game [29] .  ... 
doi:10.1371/journal.pone.0123329 pmid:26039634 pmcid:PMC4454696 fatcat:k3kjknwbwvbnrndaichav6gnp4

Congestion phenomena caused by matching pennies in evolutionary games

György Szabó, Attila Szolnoki
2015 Physical Review E  
Evolutionary social dilemma games are extended by an additional matching-pennies game that modifies the collected payoffs.  ...  Firstly, we show that the matching-pennies game can be considered as the microscopic force of the Red Queen effect that breaks the detailed balance and induces eddies in the microscopic probability currents  ...  The latter behavior reflects the fact that the matching-pennies game has only one mixed Nash equilibrium when both players choose their strategies at random.  ... 
doi:10.1103/physreve.91.032110 pmid:25871057 fatcat:cgehk4xskrbcxculq6lag6gbsy

Exploitable actions of believers in the "law of small numbers" in repeated constant-sum games

Steven Scroggin
2007 Journal of Economic Theory  
In repeated fixed-pair constant-sum games with unique equilibria in mixed strategies, such as matching 9 pennies, the subgame perfect equilibrium is repeating the stage-game mixed-strategy equilibrium  ...  Econometric model 7 I now translate the balance and runs notions that underlie local representativeness into behavioral assumptions that apply to repeated fixed-pair matching pennies games.  ...  Forty-five pairs of undergraduates from the University of Haifa played 150 rounds of matching pennies. 12 9 In both experiments, a repeated fixed-pair time series of row and column actions comes from  ... 
doi:10.1016/j.jet.2005.11.001 fatcat:gnlnaxcisvasdjaqnm7oj26as4
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