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Hard and soft preparation sets in Boolean games
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Harrenstein, Paul, Turrini, Paolo and Wooldridge, Michael (2016) Hard and soft preparation sets in Boolean games. Studia Logica, 104 (4). pp. 813-847. doi:10.1007/s11225-015-9629-9 ISSN 1572-8730.
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Official URL: http://dx.doi.org/10.1007/s11225-015-9629-9
Abstract
A fundamental problem in game theory is the possibility of reaching equi- librium 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 sat- isfaction 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 re- sponse 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.
| Item Type: | Journal Article | |||||||||
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| Subjects: | H Social Sciences > HB Economic Theory Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | |||||||||
| Library of Congress Subject Headings (LCSH): | Game theory, Economics -- Mathematical models | |||||||||
| Journal or Publication Title: | Studia Logica | |||||||||
| Publisher: | Springer | |||||||||
| ISSN: | 1572-8730 | |||||||||
| Official Date: | August 2016 | |||||||||
| Dates: |
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| Volume: | 104 | |||||||||
| Number: | 4 | |||||||||
| Page Range: | pp. 813-847 | |||||||||
| DOI: | 10.1007/s11225-015-9629-9 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 21 May 2018 | |||||||||
| Date of first compliant Open Access: | 21 May 2018 | |||||||||
| RIOXX Funder/Project Grant: |
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