Nash equilibrium and bisimulation invariance by Gutierrez, J, Harrenstein, P, Perelli, G, Wooldridge, M

Nash equilibrium and bisimulation invariance by Gutierrez, J, Harrenstein, B, Perelli, G, Wooldridge, M

Expressiveness and Nash equilibrium in iterated Boolean games by Gutierrez, J, Harrenstein, P, Perelli, G, Wooldridge, M

“…The (possibly empty) set of Nash equilibria of an iterated Boolean game can be understood as inducing a set of computations, each computation representing one way the system could evolve if players chose strategies that together constitute a Nash equilibrium. Such a set of equilibrium computations expresses a temporal property—which may or may not be expressible within a particular fragment. …”

Expressiveness and Nash equilibrium in iterated Boolean games by Gutierrez, J, Harrenstein, P, Perelli, G, Wooldridge, M

A tool for the automated verification of Nash equilibria in concurrent games by Toumi, A, Gutierrez, J, Wooldridge, M

“…The basic analytical concept for Reactive Modules Games is Nash equilibrium. In this paper, we describe a tool through which we can automatically verify Nash equilibrium strategies for Reactive Modules Games. …”

Iterated Boolean games for rational verification by Gutierrez, J, Gao, T, Wooldridge, M

“…More specifically, rational verification asks whether a given property, expressed as a temporal logic formula, is satisfied in a computation of the system that might be generated if agents within the system choose strategies for selecting actions that form a Nash equilibrium. We show that, when agents are modelled using the Simple Reactive Modules Language, a widely-used system modelling language for concurrent and multi-agent systems, this problem can be reduced to a simpler query: whether some iterated game—in which players have control over a finite set of Boolean variables and goals expressed as Linear Temporal Logic (LTL) formulae—has a Nash equilibrium. …”

Automated temporal equilibrium analysis: Verification and synthesis of multi-player games by Gutierrez, J, Najib, M, Perelli, G, Wooldridge, M

“…EVE can then check whether the Image 1 claim holds on some (or every) computation of the system that could arise through agents choosing Nash equilibrium strategies; it can also check whether a system has a Nash equilibrium, and synthesise individual strategies for players in the multi-player game. …”

From model checking to equilibrium checking: reactive modules for rational verification by Gutierrez, J, Harrenstein, B, Wooldridge, M

“…For each of these cases, after formally defining the game setting, we characterise the complexity of a range of problems relating to Nash equilibria (e.g., the computation or the verification of existence of a Nash equilibrium or checking whether a given temporal formula is satisfied on some Nash equilibrium). …”

Nash equilibria in concurrent games with lexicographic preferences by Gutierrez, J, Murano, A, Perelli, G, Rubin, S, Wooldridge, M

“…In particular, we show that deciding the existence of a strict Nash equilibrium in such games is decidable, even if players’ deviations are implemented as infinite memory strategies.…”

Reasoning about equilibria in game-like concurrent systems by Gutierrez, J, Harrenstein, P, Wooldridge, M

“…The key operator in this logic is a path quantifier [NE]ϕ, which asserts that ϕ holds on all Nash equilibrium computations of the system…”

Reasoning about equilibria in game-like concurrent systems by Gutierrez, J, Harrenstein, P, Wooldridge, M

“…The key operator in this temporal logic is a novel path quantifier [NE]ϕ, which asserts that ϕ holds on all Nash equilibrium computations of the system.…”

Electric Boolean Games: Redistribution Schemes for Resource-Bounded Agents. by Harrenstein, P, Turrini, P, Wooldridge, M

“…Different redistributions may lead to Nash equilibrium outcomes with very different properties, and so certain redistributions may be considered more attractive than others. …”

Equilibrium design for concurrent games by Gutierrez, J, Najib, M, Perelli, G, Wooldridge, M

“…In particular, we consider system specifications given by LTL and GR(1) formulae, and show that implementing a mechanism to ensure that a given temporal logic property is satisfied on some/every Nash equilibrium of the game, whenever such a mechanism exists, can be done in PSPACE for LTL properties and in NP/ΣP2 for GR(1) specifications. …”

Characterising the manipulability of Boolean games by Harrenstein, BP, Turrini, P, Wooldridge, M

“…In this paper we close this problem, giving a complete characterisation of those mechanisms that can induce a set of outcomes of the game to be exactly the set of Nash equilibrium outcomes.…”

Cooperative concurrent games by Gutierrez, J, Kowara, S, Kraus, S, Steeples, T, Wooldridge, M

“…To date, rational verification has been studied using non-cooperative solution concepts—Nash equilibrium and refinements thereof. Such non-cooperative solution concepts assume that there is no possibility of agents forming binding agreements to cooperate, and as such they are restricted in their applicability. …”

Behavioural strategies in weighted boolean games by Han, D, Harrenstein, P, Nugent, S, Philpott, J, Wooldridge, M

“…The adoption of game-theoretic models throughout artificial intelligence and computer science has prompted extensive research into algorithms and heuristics for computing game theoretic solution concepts, of which mixed strategy Nash equilibrium is one of the most prominent examples. …”