Distribution-Valued Games -- Overview, Analysis, and a Segmentation-Based Approach
Vincent B\"urgin

TL;DR
This paper formalizes distribution-valued games using stochastic orders, analyzes the properties of the tail order, identifies limitations of previous claims, and proposes a segmentation-based solution approach.
Contribution
It extends the formal framework of distribution-valued games, corrects prior misconceptions about the tail order, and introduces a novel segmentation-based solution concept.
Findings
The tail order is not total on certain distribution sets.
Not all tail-ordered games have mixed-strategy Nash equilibria.
Almost all finite-support tail-ordered games only have pure-strategy Nash equilibria.
Abstract
The paper [Ras15a] introduced distribution-valued games. This game-theoretic model uses probability distributions as payoffs for games in order to express uncertainty about the payoffs. The player's preferences for different payoffs are expressed by a stochastic order which we call the tail order. This thesis formalizes distribution-valued games with preferences expressed by general stochastic orders, and specifically analyzes properties of the tail order. It identifies sufficient conditions for tail-order preference to hold, but also finds that some claims in [Ras15a] about the tail order are incorrect, for which counter-examples are constructed. In particular, it is demonstrated that a proof for the totality of the order on a certain set of distributions contains an error; the thesis proceeds to show that the ordering is not total on the slightly less restricted set of distributions…
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Taxonomy
TopicsGame Theory and Applications · Economic theories and models · Auction Theory and Applications
