Strategic Reasoning in Automated Mechanism Design

Abstract

Mechanism Design aims at defining mechanisms that satisfy a predefined set of properties, and Auction Mechanisms are of foremost importance. Core properties of mechanisms, such as strategy-proofness or budget-balance, involve: (i) complex strategic concepts such as Nash equilibria, (ii) quantitative aspects such as utilities, and often (iii) imperfect information,with agents’ private valuations. We demonstrate that Strategy Logic provides a formal framework fit to model mechanisms, express such properties, and verify them. To do so, we consider a quantitative and epistemic variant of Strategy Logic. We first show how to express the implementation of social choice functions. Second, we show how fundamental mechanism properties can be expressed as logical formulas,and thus evaluated by model checking. Finally, we prove that model checking for this particular variant of Strategy Logic can be done in polynomial space.

Incentive Engineering for Concurrent Games

“…However, more recent works in this area adopt multi-disciplinary methods such as automated mechanism design [30,27,37,3], which typically focus on the problem of constructing incentive-compatible mechanisms to optimise a particular objective such as social welfare. Other approaches in this area reduce mechanism design to a program synthesis problem [29] or a satisfiability problem for quantitative strategy logic formulae [25,28]. The notion of dynamic incentives has also been investigated in (multi-agent) learning settings [7,26,36,42,10].…”

The Impact of Strategies and Information in Model Checking for Multi-Agent Systems

“…As promised throughout the paper, in this section, we will discuss some directions for future research. We will summarize these aspects with respect to the three main features related to the formal verification SL perfect information imperfect information memoryless -PSPACE-complete [20] memoryfull non-elementary [21] undecidable [12] Table 3: Model checking complexities for SL. of multi-agent systems, namely: strategies, information, and logics.…”

Reasoning about Human-Friendly Strategies in Repeated Keyword Auctions

“…In preliminary works, Pauly and Wooldridge [56] and Wooldridge et al [68] advocate the use of ATL [8] to reason about decision-making mechanisms. As ATL lacks the expressivity to reason about quantitative aspects such as valuations and payments, and solution concepts such as equilibria, Maubert et al [49] introduce SLK[F ], a quantitative and epistemic version of SL [26,50], and show how it can be used for reasoning about notions such as Nash equilibrium and strategyproofness. Still, their approach considers strategies as functions from states to actions and cannot handle strategies with recall.…”

“…We also assume that F contains the equality = and comparison functions <, >, ≥ (defined similarly). Finally, we assume F contains functions −, , ×, \, , and with the standard meaning (for details, see [49]). Let us fix a price increment inc ∈ (0, 1], a set of slots = {1, ..., m}, where m ∈ N \ {0}.…”