Nash equilibrium and bisimulation invariance
Game theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the possible computation runs of the system; and strategies define t...
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Conference item |
| Published: |
Leibniz International Proceedings in Informatics
2017
|
| _version_ | 1797053519225683968 |
|---|---|
| author | Gutierrez, J Harrenstein, P Perelli, G Wooldridge, M |
| author2 | Nestmann, R |
| author_facet | Nestmann, R Gutierrez, J Harrenstein, P Perelli, G Wooldridge, M |
| author_sort | Gutierrez, J |
| collection | OXFORD |
| description | Game theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the possible computation runs of the system; and strategies define the behaviour of agents. Typically, strategies are modelled as functions from sequences of system states to player actions. Analysing a system in such a way involves computing the set of (Nash) equilibria in the game. However, we show that, with respect to the above model of strategies—the standard model in the literature—bisimilarity does not preserve the existence of Nash equilibria. Thus, two concurrent games which are behaviourally equivalent from a semantic perspective, and which from a logical perspective satisfy the same temporal formulae, nevertheless have fundamentally different properties from a game theoretic perspective. In this paper we explore the issues raised by this discovery, and investigate three models of strategies with respect to which the existence of Nash equilibria is preserved under bisimilarity. We also use some of these models of strategies to provide new semantic foundations for logics for strategic reasoning, and investigate restricted scenarios where bisimilarity can be shown to preserve the existence of Nash equilibria with respect to the conventional model of strategies in the literature. |
| first_indexed | 2024-03-06T18:44:54Z |
| format | Conference item |
| id | oxford-uuid:0e299546-9538-404e-9c56-fa4760cf8915 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:44:54Z |
| publishDate | 2017 |
| publisher | Leibniz International Proceedings in Informatics |
| record_format | dspace |
| spelling | oxford-uuid:0e299546-9538-404e-9c56-fa4760cf89152022-03-26T09:44:33ZNash equilibrium and bisimulation invarianceConference itemhttp://purl.org/coar/resource_type/c_5794uuid:0e299546-9538-404e-9c56-fa4760cf8915Symplectic Elements at OxfordLeibniz International Proceedings in Informatics2017Gutierrez, JHarrenstein, PPerelli, GWooldridge, MNestmann, RMeyer, UGame theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the possible computation runs of the system; and strategies define the behaviour of agents. Typically, strategies are modelled as functions from sequences of system states to player actions. Analysing a system in such a way involves computing the set of (Nash) equilibria in the game. However, we show that, with respect to the above model of strategies—the standard model in the literature—bisimilarity does not preserve the existence of Nash equilibria. Thus, two concurrent games which are behaviourally equivalent from a semantic perspective, and which from a logical perspective satisfy the same temporal formulae, nevertheless have fundamentally different properties from a game theoretic perspective. In this paper we explore the issues raised by this discovery, and investigate three models of strategies with respect to which the existence of Nash equilibria is preserved under bisimilarity. We also use some of these models of strategies to provide new semantic foundations for logics for strategic reasoning, and investigate restricted scenarios where bisimilarity can be shown to preserve the existence of Nash equilibria with respect to the conventional model of strategies in the literature. |
| spellingShingle | Gutierrez, J Harrenstein, P Perelli, G Wooldridge, M Nash equilibrium and bisimulation invariance |
| title | Nash equilibrium and bisimulation invariance |
| title_full | Nash equilibrium and bisimulation invariance |
| title_fullStr | Nash equilibrium and bisimulation invariance |
| title_full_unstemmed | Nash equilibrium and bisimulation invariance |
| title_short | Nash equilibrium and bisimulation invariance |
| title_sort | nash equilibrium and bisimulation invariance |
| work_keys_str_mv | AT gutierrezj nashequilibriumandbisimulationinvariance AT harrensteinp nashequilibriumandbisimulationinvariance AT perellig nashequilibriumandbisimulationinvariance AT wooldridgem nashequilibriumandbisimulationinvariance |