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Discretization Drift in Two-Player Games [article]

Mihaela Rosca and Yan Wu and Benoit Dherin and David G. T. Barrett
2021 arXiv   pre-print
In particular, we identify distinct components of the discretization drift that can alter performance and in some cases destabilize the game.  ...  Gradient-based methods for two-player games produce rich dynamics that can solve challenging problems, yet can be difficult to stabilize and understand.  ...  Discretization Drift in Two-Player Games I. Experimental details I.1.  ... 
arXiv:2105.13922v2 fatcat:qkoahpvg5bczroyano47akzi2q

Towards a rigorous framework for studying 2-player continuous games

Shade T. Shutters
2013 Journal of Theoretical Biology  
Recently there has been much interest in studying the outcome of games in which players may choose a strategy from the continuous interval between extremes, requiring the set of two possible choices be  ...  prisoners dilemma actually models other games. c A favorite model of the continuous snow drift game also models other games. a b s t r a c t The use of 2-player strategic games is one of the most common  ...  Discussion Discrete 2-player games 2 Â 2 discrete games are those in which two players i and j play strategies x and y respectively.  ... 
doi:10.1016/j.jtbi.2012.12.026 pmid:23306059 fatcat:xpolrnr4erehbjj5wad3ilooye

Cooperation without Exploitation between Self-interested Agents [chapter]

Steven Damer, Maria Gini
2013 Advances in Intelligent Systems and Computing  
We study how two self-interested agents that play a sequence of randomly generated normal form games, each game played once, can achieve cooperation without being exploited.  ...  The results show that a small number of games is sufficient to achieve cooperation.  ...  We study agents that play a sequence of non-zero-sum normal form games, each game played only once by the same two players.  ... 
doi:10.1007/978-3-642-33932-5_51 fatcat:zskol54cavhjppdwkye57iflci

Estimating the probability that the game of Monopoly never ends

Eric J. Friedman, Shane G. Henderson, Thomas Byuen, German Gutierrez Gallardo
2009 Proceedings of the 2009 Winter Simulation Conference (WSC)  
We estimate the probability that the game of Monopoly between two players playing very simple strategies never ends.  ...  The simulation model is object based, and can accommodate more than two players, although we restrict attention to the two-player game in this paper.  ...  In this paper we give four different simulation-based estimators of α, assuming two-player games.  ... 
doi:10.1109/wsc.2009.5429349 dblp:conf/wsc/FriedmanHBG09 fatcat:by34dzaxzfctldjxly7owxfrvy

Cycling Co-Evolution Resulting from Genetic Adaptation in Two-Person Zero-Sum Games

David Salamon, Peter Salamon
2005 Open systems & information dynamics  
We consider two populations co-evolving with fitness defined by the payoff in a twoperson zero-sum game.  ...  We show that such situations lead to spontaneous and sustained oscillations iff the optimal strategy of the game is mixed.  ...  Palacios, and the participants in the SDSU mathematical biology seminar for helpful discussions.  ... 
doi:10.1007/s11080-005-0924-1 fatcat:3s7zt2xhsfcathb5e7pcqa6bmi

Page 823 of Mathematical Reviews Vol. , Issue 85b [page]

1985 Mathematical Reviews  
A Nash equilibrium point is described for two cases: (i) the case in which BA~? is strictly decreasing; (ii) the case in which BA~? is increasing. Extensions to n-person games are also discussed. S.  ...  New equilibrium concepts are defined for 2-person noncooperative games in which the players are allowed to change their strategies in a move-countermove arrangement.  ... 

Intrinsic Noise in Game Dynamical Learning

Tobias Galla
2009 Physical Review Letters  
Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.  ...  We here show that similar noise-sustained trajectories arise in game dynamical learning, where the stochasticity has a different origin: agents sample a finite number of moves of their opponents in-between  ...  Consider a general symmetric two-player game, played repeatedly by players X and Y , and assume there are p pure strategies in this game.  ... 
doi:10.1103/physrevlett.103.198702 pmid:20365961 fatcat:wo2mbun4kzht3fvkuhtd2x4c3i

Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations [article]

Jens Christian Claussen
2008 arXiv   pre-print
This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state.  ...  Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems.  ...  In game theory, more specific in two-player normal form games, agents 1 . . . N "play" a strategy, out of a finite set of possible pure strategies.  ... 
arXiv:0803.2443v1 fatcat:5kfud2l32na2hlkpmeykgwhwqq

Spatial games and the maintenance of cooperation

M. A. Nowak, S. Bonhoeffer, R. M. May
1994 Proceedings of the National Academy of Sciences of the United States of America  
Our earlier work, however, dealt with symmetric spatial lattices In two dimensions, deterministic winning and discrete time.  ...  We have recently proposed an alternative approach to the PD, by exploring "spatial games" in which players-who are either pure cooperators, C, or pure defectors, D-Interact with ne hbors in some spatial  ...  In its standard form, the PD is a game played by two players, each of whom may choose (independently but simultaneously) to cooperate, C, or defect, D, in any one encounter.  ... 
doi:10.1073/pnas.91.11.4877 pmid:8197150 pmcid:PMC43892 fatcat:w2rcp3jsr5cjhnecskbaxawhe4

Measuring Player's Behaviour Change over Time in Public Goods Game [chapter]

Polla Fattah, Uwe Aickelin, Christian Wagner
2017 Lecture Notes in Networks and Systems  
This problem can be considered as a concept drift problem by asking the amount of change that happens to the clusters of players over a sequence of game rounds.  ...  In this game players can be classified into different groups according to the level of their participation in the public good.  ...  ACKNOWLEDGMENT The authors record their thanks to Simon Gaechter and Felix Kolle in the School of Economics at the University of Nottingham for providing us with data from the public goods experiment and  ... 
doi:10.1007/978-3-319-56991-8_81 fatcat:cj5peessijbypgnofnqfjndada

Measuring Player's Behaviour Change over Time in Public Goods Game [article]

Polla Fattah, Uwe Aickelin, Christian Wagner
2016 arXiv   pre-print
This problem can be considered as a concept drift problem by asking the amount of change that happens to the clusters of players over a sequence of game rounds.  ...  In this game players can be classified into different groups according to the level of their participation in the public good.  ...  ACKNOWLEDGMENT The authors record their thanks to Simon Gaechter and Felix Kolle in the School of Economics at the University of Nottingham for providing us with data from the public goods experiment and  ... 
arXiv:1609.02672v1 fatcat:so6hw4xc4jcuviazdzf73lppqe

The folk theorem with imperfect public information in continuous time

Benjamin Bernard, Christoph Frei
2016 Theoretical Economics  
We prove a folk theorem for multiplayer games in continuous time when players observe a public signal distorted by Brownian noise.  ...  We study in detail the relation between behavior and mixed strategies, and the role of public randomization to move continuously across games within the same model.  ...  He studies a class of continuous-time games with two players, where the public signal is distorted by Brownian noise and players' actions affect the drift rate of the signal.  ... 
doi:10.3982/te1687 fatcat:k2mtzfbcuzgnljkgzxfcsyeobm

Integral Reinforcement Learning for Finding Online the Feedback Nash Equilibrium of Nonzero-Sum Differential Games [chapter]

Draguna Vrabie, Frank L.
2011 Advances in Reinforcement Learning  
players; b. a discrete time scale given by T 0 .  ...  In Section 3 we describe the online method that provides the Nash equilibrium solution of the two-player nonzero-sum game.  ... 
doi:10.5772/13804 fatcat:lskl23zpqbar3jststb4wj4fsa

Games with Imperfectly Observable Actions in Continuous Time

Yuliy Sannikov
2007 Econometrica  
This paper investigates a new class of 2-player games in continuous time, in which the players' observations of each other's actions are distorted by Brownian motions.  ...  These games are analogous to repeated games with imperfect monitoring in which the players take actions frequently.  ...  The partnership game belongs to a simple subclass of repeated games with two separate one-dimensional signals, whose drifts equal the actions of the two players.  ... 
doi:10.1111/j.1468-0262.2007.00795.x fatcat:uzykidkbqnchpdkfhkb23nxvsi

Page 114 of Journal of Law Economics & Organization Vol. 8, Issue 1 [page]

1992 Journal of Law Economics & Organization  
This policy, lying on the Pareto surface of the three players, represents a compromise or equilibrium of some sort among the various interests in the statute game.  ...  The enacting coalition in the statute game must, at the time of enactment, worry not only about bureaucratic discretion; they must also consider the prospect of subsequent plays of the statute game.  ... 
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