Hard and Soft Preparation Sets in Boolean Games
File(s)STUD-D-14-00081_resubmission.pdf (410.32 KB)
Accepted version
Author(s)
Harrenstein, P
Turrini, P
Wooldridge, M
Type
Journal Article
Abstract
A fundamental problem in game theory is the possibility of reaching equilibrium outcomes with undesirable properties, e.g., inefficiency. The economics literature abounds with models that attempt to modify games in order to avoid such undesirable properties, for example through the use of subsidies and taxation, or by allowing players to undergo a bargaining phase before their decision. In this paper, we consider the effect of such transformations in Boolean games with costs, where players control propositional variables that they can set to true or false, and are primarily motivated to seek the satisfaction of some goal formula, while secondarily motivated to minimise the costs of their actions. We adopt (pure) preparation sets (prep sets) as our basic solution concept. A preparation set is a set of outcomes that contains for every player at least one best response to every outcome in the set. Prep sets are well-suited to the analysis of Boolean games, because we can naturally represent prep sets as propositional formulas, which in turn allows us to refer to prep formulas. The preference structure of Boolean games with costs makes it possible to distinguish between hard and soft prep sets. The hard prep sets of a game are sets of valuations that would be prep sets in that game no matter what the cost function of the game was. The properties defined by hard prep sets typically relate to goal-seeking behaviour, and as such these properties cannot be eliminated from games by, for example, taxation or subsidies. In contrast, soft prep sets can be eliminated by an appropriate system of incentives. Besides considering what can happen in a game by unrestricted manipulation of players’ cost function, we also investigate several mechanisms that allow groups of players to form coalitions and eliminate undesirable outcomes from the game, even when taxes or subsidies are not a possibility.
Date Issued
2015-09-23
Date Acceptance
2015-09-23
Citation
Studia Logica, 2015, 104 (4), pp.813-847
ISSN
1572-8730
Publisher
Springer Verlag
Start Page
813
End Page
847
Journal / Book Title
Studia Logica
Volume
104
Issue
4
Copyright Statement
© Springer Verlag 2016. The final publication is available at Springer via http://dx.doi.org/10.1007/s11225-015-9629-9
Subjects
General Mathematics
01 Mathematical Sciences
08 Information And Computing Sciences
22 Philosophy And Religious Studies
Publication Status
Published