We propose and experimentally test a mechanism for a class of principal-agent problems in which agents can observe each others' efforts. In this mechanism each player costlessly assigns a share of the pie to each of the other players, after observing their contributions, and the final distribution is determined by these assignments. We show that cooperation can be achieved under this simple mechanism and, in a controlled laboratory experiment, we find that players use a proportional rule to reward others in most cases and that the players' contributions improve substantially and almost immediately with 80% of players contributing fully.
While the assumption of infinity is prevalent in almost every area of economics, for two well-known frameworks in decision theory, we note some fundamental differences between the finite versions and their infinite counterpart. The first is on the usage of mixed strategies in finite games, while the second is on a characterization of the truth axiom in models of information and knowledge, where the properties of belief can be related to the properties of preference.
In a recent paper Xie et al. (Fixed Point Theory Appl. 2013:192, 2013 gave several extensions and some applications of the Abian-Brown (AB) fixed point theorem. While the AB fixed point theorem and its extensions (as well as other related fixed point theorems) assume that the mapping is isotone, this note shows that for single-valued finite maps this condition relates to the acyclicity of the map, which in turn relates to Abian's (Nieuw Arch. Wiskd. XVI:184-185, 1968) most basic fixed point theorem for finite sets. MSC: 46B42; 47H10; 58J20; 91A06; 91A10
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