Iterated Boolean games

Abstract

Iterated games are well-known in the game theory literature. We study iterated Boolean games. These are games in which players repeatedly choose truth values for Boolean variables they have control over. Our model of iterated Boolean games assumes that players have goals given by formulae of Linear Temporal Logic (LTL), a formalism for expressing properties of state sequences. In order to represent the strategies of players in such games, we use a finite state machine model. After introducing and formally defining iterated Boolean games, we investigate the computational complexity of their associated game-theoretic decision problems, as well as semantic conditions characterising classes of LTL properties that are preserved by equilibrium points (pure-strategy Nash equilibria) whenever they exist.

Reasoning about equilibria in game-like concurrent systems

“…Remark 8. Observe that the reactive games model strictly generalises the iBG model (Gutierrez, Harrenstein, and Wooldridge 2013), which can be represented as a reactive game where the arena is an implicitly defined clique whose nodes are the valuations of the variables the players control, goals are LTL formulae, and strategies are deterministic.…”

“…will be generated in equilibrium? In (Gutierrez, Harrenstein, and Wooldridge 2013), this question was investigated using the Iterated Boolean Games (iBG) model. In this model, each player is assumed to control a set of Boolean variables, and the game is played over an infinite sequence of rounds, where at each round every player chooses values for its variables.…”

“…Each player has a goal, expressed as an LTL formula, and acts strategically in pursuit of this goal. Given this, some computations of a game can be identified as being the result of Nash equilibrium strategies, and (Gutierrez, Harrenstein, and Wooldridge 2013) suggested that the key questions in the strategic analysis of the system are whether a given LTL formula holds in some or all equilibrium computations.…”

“…While the iBG model of (Gutierrez, Harrenstein, and Wooldridge 2013) is useful for the purposes of exposition, it is not a realistic model of concurrent programs. Moreover, (Gutierrez, Harrenstein, and Wooldridge 2013) provides no language for reasoning about the equilibria of systems: such reasoning must be carried out at the meta-level.…”

“…Moreover, (Gutierrez, Harrenstein, and Wooldridge 2013) provides no language for reasoning about the equilibria of systems: such reasoning must be carried out at the meta-level. This paper fills those gaps.…”