Probabilistic Verification for Obviously Strategyproof Mechanisms

Obviously strategyproof (OSP) mechanisms maintain the incentive compatibility of agents that are not fully rational. They have been object of a number of studies since their recent definition. We are motivated by the result showing that OSP mechanisms without money cannot return good approximations, even if the designer monitors the agents during the execution of the mechanism We ask whether there are different (harsher) forms of punishments and novel ways to exert control over the agents that can overcome this impossibility. We define a model of probabilistic verification wherein agents are caught misbehaving with a certain probability and show how OSP mechanisms without money can implement a given social choice function at the cost of either imposing very large fines for lying or verifying a linear number of agents

Two-way Greedy: Algorithms for Imperfect Rationality

The realization that selfish interests need to be accounted for in the design of algorithms has produced many contributions in computer science under the umbrella of algorithmic mechanism design. Novel algorithmic properties and paradigms have been identified and studied. Our work stems from the observation that selfishness is different from rationality; agents will attempt to strategize whenever they perceive it to be convenient according to their imperfect rationality. Recent work has focused on a particular notion of imperfect rationality, namely absence of contingent reasoning skills, and defined obvious strategyproofness (OSP) as a way to deal with the selfishness of these agents. Essentially, this definition states that to care for the incentives of these agents, we need not only pay attention about the relationship between input and output, but also about the way the algorithm is run. However, it is not clear what algorithmic approaches must be used for OSP. In this paper, we show that, for binary allocation problems, OSP is fully captured by a combination of two well-known algorithmic techniques: forward and reverse greedy. We call two-way greedy this algorithmic design paradigm. Our main technical contribution establishes the connection between OSP and two-way greedy. We build upon the recently introduced cycle monotonicity technique for OSP. By means of novel structural properties of cycles and queries of OSP mechanisms, we fully characterize these mechanisms in terms of extremal implementations. These are protocols that ask each agent to consistently separate one extreme of their domain at the current history from the rest. Through the connection with the greedy paradigm, we are able to import a host of approximation bounds to OSP and strengthen the strategic properties of this family of algorithms. Finally, we begin exploring the power of two-way greedy for set systems