Endogenous games with goals: side-payments among goal-directed agents

摘要

Boolean games have been developed as a paradigm for modelling societies of goal-directed agents. In boolean games agents exercise control over propositional variables and strive to achieve a goal formula whose realization might require the opponents’ cooperation. The presence of agents that are goal-directed makes it difficult for an external authority to be able to remove undesirable properties that are inconsistent with agents’ goals, as shown by recent contributions in the multi-agent literature. What this paper does is to analyse the problem of regulation of goal-direct agents from within the system, i.e., what happens when agents themselves are given the chance to negotiate the strategies to be played with one another. Concretely, we introduce endogenous games with goals, obtained coupling a general model of goal-directed agents (strategic games with goals) with a general model of pre-play negotiations (endogenous games) coming from game theory. Strategic games with goals are shown to have a direct correspondence with strategic games (Proposition 1) but, when side-payments are allowed in the pre-play phase, display a striking imbalance (Proposition 4). The effect of side-payments can be fully simulated by taxation mechanisms studied in the literature (Proposition 7), yet we show sufficient conditions under which outcomes can be rationally sustained without external intervention (Proposition 5). Also, integrating taxation mechanisms and side-payments, we are able to transform our starting models in such a way that outcomes that are theoretically sustainable thanks to a pre-play phase can be actually sustained even with limited resources (Proposition 8). Finally, we show how an external authority incentivising a group of agents can be studied as a special agent of an appropriately extended endogenous game with goals (Proposition 11).