7,524 research outputs found
On the existence of Nash equilibria in strategic search games
We consider a general multi-agent framework in which a set of n agents are roaming a network where m valuable and sharable goods (resources, services, information ....) are hidden in m different vertices of the network. We analyze several strategic situations that arise in this setting by means of game theory. To do so, we introduce a class of strategic games that we call strategic search games. In those games agents have to select a simple path in the network that starts from a predetermined set of initial vertices. Depending on how the value of the retrieved goods is splitted among the agents, we consider two game types: finders-share in which the agents that find a good split among them the corresponding benefit and firsts-share in which only the agents that first find a good share the corresponding benefit. We show that finders-share games always have pure Nash equilibria (pne ). For obtaining this result, we introduce the notion of Nash-preserving reduction between strategic games. We show that finders-share games are Nash-reducible to single-source network congestion games. This is done through a series of Nash-preserving reductions. For firsts-share games we show the existence of games with and without pne. Furthermore, we identify some graph families in which the firsts-share game has always a pne that is computable in polynomial time.Peer ReviewedPostprint (author’s final draft
Axiomatic Approach to Solutions of Games
We consider solutions of normal form games that are invariant under strategic
equivalence. We consider additional properties that can be expected (or be
desired) from a solution of a game, and we observe the following:
- Even the weakest notion of individual rationality restricts the set of
solutions to be equilibria. This observation holds for all types of solutions:
in pure-strategies, in mixed strategies, and in correlated strategies where the
corresponding notions of equilibria are pure-Nash, Nash and coarse-correlated.
An action profile is (strict) simultaneous maximizer if it simultaneously
globally (strictly) maximizes the payoffs of all players.
- If we require that a simultaneous maximizer (if it exists) will be a
solution, then the solution contains the set of pure Nash equilibria.
- There is no solution for which a strict simultaneous maximizer (if it
exists) is the unique solution
Efficient Local Search in Coordination Games on Graphs
We study strategic games on weighted directed graphs, where the payoff of a
player is defined as the sum of the weights on the edges from players who chose
the same strategy augmented by a fixed non-negative bonus for picking a given
strategy. These games capture the idea of coordination in the absence of
globally common strategies. Prior work shows that the problem of determining
the existence of a pure Nash equilibrium for these games is NP-complete already
for graphs with all weights equal to one and no bonuses. However, for several
classes of graphs (e.g. DAGs and cliques) pure Nash equilibria or even strong
equilibria always exist and can be found by simply following a particular
improvement or coalition-improvement path, respectively. In this paper we
identify several natural classes of graphs for which a finite improvement or
coalition-improvement path of polynomial length always exists, and, as a
consequence, a Nash equilibrium or strong equilibrium in them can be found in
polynomial time. We also argue that these results are optimal in the sense that
in natural generalisations of these classes of graphs, a pure Nash equilibrium
may not even exist.Comment: Extended version of a paper accepted to IJCAI1
CP-nets and Nash equilibria
We relate here two formalisms that are used for different purposes in
reasoning about multi-agent systems. One of them are strategic games that are
used to capture the idea that agents interact with each other while pursuing
their own interest. The other are CP-nets that were introduced to express
qualitative and conditional preferences of the users and which aim at
facilitating the process of preference elicitation. To relate these two
formalisms we introduce a natural, qualitative, extension of the notion of a
strategic game. We show then that the optimal outcomes of a CP-net are exactly
the Nash equilibria of an appropriately defined strategic game in the above
sense. This allows us to use the techniques of game theory to search for
optimal outcomes of CP-nets and vice-versa, to use techniques developed for
CP-nets to search for Nash equilibria of the considered games.Comment: 6 pages. in: roc. of the Third International Conference on
Computational Intelligence, Robotics and Autonomous Systems (CIRAS '05). To
appea
Competition for order flow as a coordination game
Competition for order flow can be characterized as a coordination game with multiple equilibria. Analyzing competition between dealer markets and a crossing network, we show that the crossing network is more stable for lower traders’ disutilities from unexecuted orders. By introducing private information, we prove existence of a unique equilibrium with market consolidation. Assets with low volatility and large volumes are traded on crossing networks, others on dealer markets. Efficiency requires more assets to be traded on crossing networks. If traders’ disutilities differ sufficiently, a unique equilibrium with market fragmentation exists. Low disutility traders use the crossing network while high disutility traders use the dealer market. The crossing network’s market share is inefficiently small
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