Boolean Games with Epistemic Goals

Abstract

Abstract. We introduce and formally study games in which the goals of players relate to the epistemic states of players in the game. For example, one player might have a goal that another player knows a certain proposition, while another player might have as a goal that a certain player does not know some proposition. The formal model we use to study epistemic games is a variation of the increasingly popular Boolean games model in which each player controls a number of Boolean variables, but has limited ability to see the truth values of the overall set of formulae that hold in the game. Each player in an epistemic Boolean game has a goal, defined as a formula of modal epistemic logic. Using such a language for goals allows us to explicitly and compactly represent desirable epistemic states. After motivating and formally defining epistemic Boolean games as a concise representation of epistemic Kripke structures, we investigate their complexity and study their properties.

Modelling incomplete information in Boolean games using possibilistic logic

“…all agents know that they are PNEs and all agents know that all agents know that they are PNEs etc. The same authors have extended this framework to epistemic Boolean games [9], in which the logical language for describing goals is broadened to a multi-agent epistemic modal logic. Note, however, that agents are still fully aware of each other's goals in this framework, i.e.…”

“…Note, however, that agents are still fully aware of each other's goals in this framework, i.e. [9] considers agents whose goal is to obtain a particular epistemic state. For instance, I not only want my husband to pick up our baby, I also want to know he is picking up our baby.…”

“…For every j / ∈ eq(U(ν), U(ν )) such that u j (ν ) < u j (ν) holds, the definition of co(i, ν) (9) implies that u j (ν ) > u i (ν). Moreover, (9) implies that i / ∈ eq(U(ν), U(ν )). Consequently, we have u j (ν ) > min j / ∈eq(U (ν),U (ν )) u j (ν).…”

Simulating cardinal preferences in Boolean games: A proof technique

“…Boolean games proved to be a popular framework for modelling aspects of multiagent systems such as incentive design (Wooldridge, 2012;Endriss et al, 2011;Levit et al, 2013;Turrini, 2013;Galafassi and Bazzan, 2013;Harrenstein et al, 2014), coalition formation (Dunne et al, 2008;Bonzon et al, 2012;Popovici and Dobre, 2012), delegation (Kraus and Wooldridge, 2012) and communication (Grant et al, 2011). However, the inability of agents in Boolean games to express preferences other than { 0, 1 } was a hindrance in this setting, and a number of frameworks sought to enrich the players' preferences by description logics (Lukasiewicz and Ragone, 2009), CP-nets, (Bonzon et al, 2009c,a), modal logics (Gutierrez et al, 2013;Ågotnes et al, 2013;Harrenstein et al, 2015), fuzzy logics (Marchioni and Wooldridge, 2014), and formula weights (Bilò, 2007;Mavronicolas et al, 2007). While this line of work may appear to resemble the main thrust of this paper, we stress the crucial difference: the above works extended the Boolean games framework into something different.…”

Possibilistic Boolean Games: Strategic Reasoning under Incomplete Information

“…all agents know that they are PNEs and all agents know that all agents know that they are PNEs etc. The same authors have extended this framework to epistemic BGs [1], in which the logical language for describing goals is broadened to a multi-agent epistemic modal logic. Note, however, that agents are still completely aware of each others' goals in this framework.…”