Similarities in axiomatizations: equal surplus division value and first-price auctions
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Similarities in axiomatizations: equal surplus division value and first-price auctions Takumi Kongo1 Received: 7 January 2020 / Accepted: 5 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We compare axiomatizations between a value for cooperative games with transferable utilities (TU games), and a rule for auctions. The equal surplus division value on the set of zero-monotonic TU games is characterized by the following: individual rationality, Pareto efficiency, and equal effect of players’ nullification on others. Meanwhile, first-price auctions, on the general preference domain, are characterized by individual rationality, envy-freeness, and weak equal effect of buyers’ nullification on others. Here, envy-freeness implies Pareto efficiency in the model of auctions. Given the agents’ general preferences in the auction model, the characteristic of a weak equal effect of buyers’ nullification on others weakens the requirement of equal effect of players’ nullification on others. Although the two models are different, the corresponding axioms in both models require conditions corresponding to each other. In particular, individual rationality requires voluntary participation of agents, Pareto efficiency (or its stronger axiom of envy-freeness in the model of auctions) requires outcomes with no waste, and (weak) equal effect of players’ (buyers’) nullification on others requires equal treatment of agents when an agent is nullified. Therefore, in terms of axiomatizations, we can similarly interpret the equal surplus division value and first-price auctions. Keywords Axiomatization · Equal surplus division value · First-price auction · Nullification JEL Classification C71 · D44 · D82
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Takumi Kongo [email protected] Faculty of Economics, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan
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T. Kongo
1 Introduction In a society, there are various allocation problems which involve the allocation of something, whether a good or service, between multiple, interacting agents. Among such problems, cooperative games with transferable utilities (henceforth, TU games) focus on the situations in which players form a group and divide the benefits generated by the group. Solutions to TU games are values that determine a specific allocation of the good or service based on players’ productivity in each game. Among the possible values for TU games, the equal surplus division value (Driessen and Funaki 1991) offers each player the worth of one’s singleton coalition in addition to equal division of the surplus obtained by all players. Auctions are also allocation problems among multiple agents. In an auction, each buyer has their preferences on the set of allotments. Allotments are pairs of the state of obtaining or not obtaining the auctioned item, and the amount of money paid in each case.1 Solutions to an auction model are rules that determine allotments for all buyers, based on buyers’ preferences in each auction. First-price auctions, considering a single item auctio
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