An indirect evolutionary justification of risk neutral bidding in fair division games
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An indirect evolutionary justification of risk neutral bidding in fair division games Werner Güth1,2 · Paul Pezanis-Christou3 Accepted: 29 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We justify risk neutral equilibrium bidding in commonly known fair division games with incomplete information by an evolutionary setup postulating (i) minimal common knowledge, (ii) optimal responses to conjectural beliefs how others behave and (iii) evolutionary selection of conjectural beliefs with fitness measured by expected payoffs. After justifying the game forms we derive the evolutionary games for firstand second-price fair division and determine the evolutionarily stable conjectures. The latter coincide with equilibrium bidding, irrespectively of the number of bidders, i.e., heuristic belief adaptation can imply the same bidding behavior as equilibrium analysis based on common knowledge and counterfactual bidding. Keywords Fair division · Evolutionary stable strategies · Risk neutrality
1 Introduction Unlike auctions, fair division considers closed group interaction: there is no outside party, like sellers (in standard auctions) or buyers (in procurement auctions), confronting bidders. Typical examples of such situations are divorce and inheritance settlements in private life, regulated in family law, and terminating joint venture firms
We thank an anonymous referee for useful comments. Support from the Max Planck Institute for Research on Collective Goods and the Australian Research Council (DP140102949) is gratefully acknowledged. The usual disclaimer applies.
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Paul Pezanis-Christou [email protected] Werner Güth [email protected]
1
Max Planck Institute for Research on Collective Goods, Bonn, Germany
2
LUISS, Rome, Italy
3
School of Economics, University of Adelaide, Adelaide, Australia
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with rules in commerce. When privately arranged conflict resolution fails, the involved parties often appeal to legal conflict resolution according to regulations in family law or commercial law which usually rely on bidding. Güth and van Damme (1986) and Cramton et al. (1987) have modelled these as games under incomplete information and shown how they relate to bidding. McAfee (1992) and Morgan (2004) compare firstand second-price fair division games to other procedures and de Frutos (2000) extends the analysis to asymmetric cases. Moldovanu (2002) reviews the literature on partnership dissolution when private information is not independent. A common feature of these studies is that equilibrium bidding hinges upon a commonly known prior about bidders’ private information. Following Vickrey (1961) and Harsanyi (1967, 1968a, b), private value information is captured by a commonly known fictitious chance move about whose results the interacting parties are privately informed. This simply means that chance randomly selects a vector of individual values according to a commonly known probability distribution and that each party only learns about its own
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