Abstract
We study a non-symmetric variant of General Lotto games introduced in Hart (Int J Game Theory 36:441–460, 2008). We provide a complete characterization of optimal strategies for both players in non-symmetric discrete General Lotto games, where one of the players has an advantage over the other. By this we complete the characterization given in Hart (Int J Game Theory 36:441–460, 2008), where the strategies for symmetric case were fully characterized and some of the optimal strategies for the non-symmetric case were obtained. We find a group of completely new atomic strategies, which are used as building components for the optimal strategies. Our results are applicable to discrete variants of all-pay auctions.
Highlights
1 Introduction General Lotto games are allocation games introduced in Hart (2008) as a technical tool for studying Colonel Blotto games
The Colonel Blotto game is a classic example of allocation games, where two players compete on different fronts allocating to them their limited resources
In this paper we have found the missing optimal strategies for the players in non-symmetric Discrete General Lotto games
Summary
General Lotto games are allocation games introduced in Hart (2008) as a technical tool for studying Colonel Blotto games. Sahuguet and Persico (2006) connect the non-symmetric General Lotto games to complete information all-pay auctions, as studied by Baye et al (1996) In this kind of auctions equilibria in pure strategies do not exist. In this paper we fill in the missing cases by providing complete characterization of the optimal strategies in discrete General Lotto games Such a characterization is useful for the following reasons. As we discussed above, General Lotto games are of interest on their own, due to their connection to political economics and multiobject auctions In these applications a continuous variant was mostly used, in most cases it should be considered as a simplification, as usually there exists a minimal unit of exchange, and agents cannot propose any real number (e.g. as their promises to electorate). The Appendix contains a more technical part of the proofs
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