Dominant Strategies and Direct Mechanisms

In this chapter we will study the implementation of social choice functions by means of dominant strategies. Our first result is the so-called Revelation Principle which says that a necessary condition for implementation in dominant strategies is that there exist a direct mechanism — that is, a mechanism where each agent announces her characteristic — for which to reveal the true characteristic is a dominant strategy, in other words, truth-telling is an equilibrium (Proposition 1). We will also see how, if truth-telling is a dominant strategy, it is a Nash equilibrium and vice versa (Proposition 2). In section 3.3 we will study the incentives to tell the truth in economic environments. We will prove that under reasonable conditions there is no truth-telling mechanism, either in private good economies or in public good economies (Propositions 3 and 4). In section 3.4 we will see how if the preferences are quasi-linear and the full Pareto efficiency of the allocation as well as the individual rationality of the outcomes are not required, there is a mechanism in which the truth is a dominant strategy and the decision regarding the public good is optimal (Proposition 5). Under some additional conditions this mechanism is unique (Proposition 6). However, if individual rationality is assumed, any mechanism which induces truth-telling will almost always produce inefficient results (Proposition 7). Finally, section 3.5 is devoted to studying the incentives to reveal the true initial endowments also with similar negative results (Proposition 8).