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Tributes to Bill Sandholm

1. 

Tohoku University, Graduate School of Economics and Management and Research Center for Policy Design, Kawauchi 27-1, Aoba-ku, Sendai, Miyagi 980-8576, Japan

2. 

University of Tsukuba, Department of Policy and Planning Sciences, Tennoudai 1-1-1, Tsukuba, Ibaraki 305-8573, Japan

3. 

Shanghai University of Finance and Economics, School of Economics, 111 Wuchuan Road, Shanghai 200433, China

4. 

Ashoka University, Department of Economics, Sonipat, Haryana 131029, India

5. 

University of Oregon, Department of Economics, 1285 University of Oregon, Eugene, OR 97403, USA

*Corresponding author: Dai Zusai

Received  December 2020 Revised  March 2022 Early access May 2022

Fund Project: This work is supported by grants-in-aid for open access from Graduate School of Economics and Management, Tohoku University

In this paper, former students of Bill Sandholm provide summaries of Bill's academic contributions as a unifier of evolutionary game theory and also share their personal memories with Bill as a kind, friendly and dedicated mentor. The paper consists on five essays; first on the unification of EGT with the concept of revision protocols and his charming personality, second on stochastic dynamics, third on potential games, fourth on geometric aspects of Bill's analysis, especially on the projection dynamic, and fifth on applications to cultural evolution.

Citation: Dai Zusai, Ryoji Sawa, Man Wah Cheung, Ratul Lahkar, Jiabin Wu. Tributes to Bill Sandholm. Journal of Dynamics and Games, doi: 10.3934/jdg.2022009
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show all references

References:
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D. Acemoglu and J. Robinson, Why Nations Fail: The Origins of Power, Prosperity and Poverty, Crown Business, 2012. Available from: https://books.google.co.jp/books?id=PLlOCUIAh88C.

[2]

T. Akamatsu, T. Mori, M. Osawa and Y. Takayama, Multimodal agglomeration in economic geography, preprint, 2021, arXiv: 1912.05113. doi: 10.13140/RG.2.2.26869.32488.

[3]

T. Akamatsu and K. Wada, Tradable network permits: A new scheme for the most efficient use of network capacity, Trans. Res. Part C Emerg. Tech., 79 (2017), 178-195.  doi: 10.1016/j.trc.2017.03.009.

[4]

E. Akin, Domination or equilibrium, Math. Biosci., 50 (1980), 239-250.  doi: 10.1016/0025-5564(80)90039-5.

[5] E. Akin, The Geometry of Population Genetics, Lecture Notes in Biomathematics, 31, Springer-Verlag, Berlin-New York, 1979. 
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C. Alós-Ferrer and N. Netzer, Robust stochastic stability, Econom. Theory, 58 (2015), 31-57.  doi: 10.1007/s00199-014-0809-z.

[7]

C. Alós-Ferrer and I. Neustadt, Best-response dynamics in a birth-death model of evolution in games, Int. Game Theory Rev., 12 (2010), 197-204.  doi: 10.1142/S021919891000260X.

[8]

C. Alós-Ferrer and S. Weidenholzer, Partial bandwagon effects and local interactions, Games Econom. Behav., 61 (2007), 179-197.  doi: 10.1016/j.geb.2007.01.007.

[9]

S. Arigapudi, Exit from equilibrium in coordination games under probit choice, Games Econom. Behav., 122 (2020), 168-202.  doi: 10.1016/j.geb.2020.04.003.

[10]

S. Arigapudi, Transitions between equilibria in bilingual games under logit choice, J. Math. Econom., 86 (2020), 24-34.  doi: 10.1016/j.jmateco.2019.10.004.

[11]

D. BalkenborgJ. Hofbauer and C. Kuzmics, Refined best reply correspondence and dynamics, Theor. Econ., 8 (2013), 165-192.  doi: 10.3982/TE652.

[12]

M. Benaïm and M. W. Hirsch, Mixed equilibria and dynamical systems arising from fictitious play in perturbed games, Games Econom. Behav., 29 (1999), 36-72.  doi: 10.1006/game.1999.0717.

[13]

M. BenaïmJ. Hofbauer and S. Sorin, Stochastic approximations and differential inclusions, SIAM J. Control Optim., 44 (2005), 328-348.  doi: 10.1137/S0363012904439301.

[14]

M. Benaïm and J. W. Weibull, Deterministic approximation of stochastic evolution in games, Econometrica, 71 (2003), 873-903.  doi: 10.1111/1468-0262.00429.

[15]

K. Binmore and L. Samuelson, Muddling through: Noisy equilibrium selection, J. Econom. Theory, 74 (1997), 235-265.  doi: 10.1006/jeth.1996.2255.

[16]

A. Bisin and T. Verdier, The economics of cultural transmission and the dynamics of preferences, J. Econom. Theory, 97 (2001), 298-319.  doi: 10.1006/jeth.2000.2678.

[17]

T. Börgers and R. Sarin, Learning through reinforcement and replicator dynamics, J. Econom. Theory, 77 (1997), 1-14.  doi: 10.1006/jeth.1997.2319.

[18]

M.-W. Cheung, Imitative dynamics for games with continuous strategy space, Games Econom. Behav., 99 (2016), 206-223.  doi: 10.1016/j.geb.2016.08.003.

[19]

M.-W. Cheung, Pairwise comparison dynamics for games with continuous strategy space, J. Econom. Theory, 153 (2014), 344-375.  doi: 10.1016/j.jet.2014.07.001.

[20]

M.-W. Cheung and R. Lahkar, Nonatomic potential games: The continuous strategy case, Games Econom. Behav., 108 (2018), 341-362.  doi: 10.1016/j.geb.2017.12.004.

[21]

M.-W. Cheung and J. Wu, On the probabilistic transmission of continuous cultural traits, J. Econom. Theory, 174 (2018), 300-323.  doi: 10.1016/j.jet.2018.01.002.

[22]

E. Dokumacı and W. H. Sandholm, Large deviations and multinomial probit choice, J. Econom. Theory, 146 (2011), 2151-2158.  doi: 10.1016/j.jet.2011.06.013.

[23]

E. Dokumacı and W. H. Sandholm, Schelling redux: An evolutionary dynamic model of residential segregation, to appear, J. Dyn. Games. doi: 10.3934/jdg.2022006.

[24]

J. C. Ely and W. H. Sandholm, Evolution in Bayesian games. I. Theory, Games Econom. Behav., 53 (2005), 83-109.  doi: 10.1016/j.geb.2004.09.003.

[25]

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Figure 1.  Structural framework
Figure 2.  Bill Sandholm with young scholars at a bar in Lund, Sweden, on the final day of Learning, Evolution and Games conference in 2018. He was with Ryoji Sawa, Segis and Luis Izquierdo, Erik Mohlin and Alex Rigos, as well as Dai behind the camera
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