Efficient Auctions with Altruism∗ Ruggiero Cavallo Microsoft Research 1290 Avenue of the Americas, 6th floor New York, NY 10104 [email protected] September 6, 2012 Abstract We introduce a novel regret-based model of altruism, wherein agents are willing to forgo a small amount of value if doing so increases social welfare, and consider its implications in a single-item allocation setting. We demonstrate that even for very mildly altruistic agents classic approaches such as VCG are manipulable, but straightforward variants of known mechanisms that are strategyproof in the purely-selfish case succeed in achieving dominant strategy efficiency and strong budget-balance, i.e., full social welfare for the group, a result unachievable in the case of completely selfish agents. We contrast this positive result with a negative analysis of a more traditional (non-regret- based) altruism model, demonstrating that nothing short of complete altruism yields existence of a strongly budget-balanced efficient mechanism there. JEL Classification: D64, D44, D01, D82 1 Introduction Mechanism design is a cynical enterprise: the goal is to derive schemes under which selfish agents, unconcerned with the welfare of others, cannot benefit from doing other than what is considered optimal from a social perspective (e.g., truthfully reporting private information to allow identification of a social welfare maximizing action). When such schemes succeed in simultaneously satisfying the goals of the social planner and each agent, the assumption of selfishness makes them robust. But unfortunately often they cannot succeed; most notably, efficient mechanisms in ∗A significant portion of this work was completed while the author was a postdoctoral fellow at the University of Pennsylvania. 1 which individuals in the group retain all value from the chosen outcome do not exist, even for very simple restricted settings. So mechanism design is cynical because built into its framework is the selfishness assumption and its dark consequence: that efficient decision making is impossible. But in the real world the situation may not be so dark. The main observation of this paper is that, at least in some important settings, small amounts of the right kind of altruism can go a long way in achieving an efficient framework for group decision-making. The positive contribution here lies primarily not in design of a mechanism that dramatically deviates from previously known schemes; rather it lies in identification of reasonable characteristics of agent utility functions that, when present, allow simple variants on known schemes to bring success. Specifically, when agents are altruistic in a regret-based way, indifferent between giving up a small amount of value for the good of the group and not, budget-balanced and efficient single-item auctions exist. In environments where transferring money outside the group of agents is a loss that detracts from social welfare, true efficiency requires strong budget-balance, and this is not attainable in the purely selfish setting. The positive results we obtain for single-item allocation are paired with negative results for more general decision settings, and strong negative results—even in the single-item allocation case—for a more traditional (non-regret-based) model of altruism wherein each agent’s utility is a weighted linear combination of the values obtained by individuals in the group. This justifies the focus on a regret-based altruism notion, despite the fact that—like any specific utility model—it will not always apply. The following list summarizes the main contributions of the paper: • We introduce a regret-based model of altruism, capturing the idea that indi- viduals may be willing to give up a certain fixed amount of value for the good of the group, and use it to exactly characterize the degree of altruism that is necessary and sufficient for dominant strategy implementation of a class of efficient mechanisms. • We demonstrate that when agents are even slightly altruistic, mechanisms that are strategyproof in the case of selfish agents become manipulable (Proposition 3). • We present a strongly budget-balanced variant of the redistribution mechanism of Cavallo (2006), and demonstrate that in single-item allocation settings it is efficient in dominant strategies and ex post individually rational if agents are “mildly” altruistic (i.e., if for the good of the group they are willing to give up an amount of utility that is small compared to the expected utility they obtain) (Theorem 2). • We demonstrate that this positive result does not extend from allocations to general, unrestricted types settings (Theorem 4). 2 • We consider the historically more standard non-regret-based model of altruism in which an agent’s utility is a linear combination of his own value and that of the other agents. We demonstrate that no anonymous, strongly budget- balanced, dominant strategy efficient mechanism exists unless agents are com- pletely altruistic in this model (Theorem 5). • We consider the case of “proportionally altruistic” agents: those that are willing to give up a certain percentage of the maximum selfish utility they could obtain. We show that the mechanisms successful for our first altruism model fail here, but we also present a simple alternative mechanism demonstrating that—unlike in the case of non-regret-based altruism—efficiency is possible for small groups of moderately (rather than completely) proportionally-altruistic agents (Theorem 7). In the rest of this section we provide background and discuss related work. In Section 2 we introduce our model of altruism, starting with a general class of other-regarding utility functions and moving on to specific instances; here we also demonstrate the failure of previous mechanisms. (Readers well-informed of the relevant mechanism design literature may wish to skip Section 1.2.) In Section 3 we present solutions: efficient and strongly budget-balanced mechanisms for single-item allocation. In Section 4 we consider several natural generalizations. We end with a discussion in Section 5. 1.1 Altruism and mechanism design The enterprise of mechanism design is situated in a context of game-theoretic agents, each of whom acts in a way that maximizes some individual utility function. The agents hold private information that is critical to evaluating any potential decision; agents are asked to make claims about their private information and a decision is made. The goal of a direct mechanism is to align agent incentives towards a desired objective, such as social welfare maximization, so that they will truthfully reveal their private information and an optimal choice can be identified. The tool used for this purpose is monetary payments. The classical setting is one in which utility functions are quasilinear, with each agent’s utility independent of the payments imposed on other agents. However, to state the obvious, there is abundant evidence that people—as opposed, say, to corporations—are often concerned with the welfare of others (see, e.g., Andreoni and Miller (2002) or Charnes and Rabin (2002) for empirical evidence in an economic setting), and in such settings new approaches are required. Before presenting the relevant background in classical mechanism design, we draw attention to related work that considers agents that are not fully self-interested. Bowles and Hwang (2008) provide an analysis of the provision of optimal incen- tives in a mechanism design setting taking into account factors such as reciprocity, 3 intrinsic motivation, and respect for ethical norms. Their work is a response to compelling evidence that monetary incentives frequently either undermine or ex- aggerate individuals’ inherent inclination to be “civic-minded”. Incentives may in- hibit altruism by signaling that self-interested behavior is expected (Hoffman et al, 1994; Irlenbusch and Sliwka, 2005) or by diminishing individual feelings of self- determination (Deci et al, 1999) (but see Cameron et al (2001) for a counter- perspective); they may directly signal the mechanism designer’s preferences and in so doing undermine individuals’ valuation of the desired behavior (Benabou and Tirole, 2003; Seabright, 2004); or they may promote altruism via trust and bandwagon effects that result when individuals take incentives as indication that others will behave altruistically (Shinada and Yamagishi, 2007). Charnes and Rabin (2002) obtain evidence of social-welfare-motivated behavior in simple money-allocation be- havioral experiments. Frey and Jegen (2001) is a good survey of this type of empir- ical evidence; for a broader view including ethnographic studies, see Henrich et al (2004). Chen and Kempe (2008) analyze how the price of anarchy in a traffic-routing network problem changes if one refrains from assuming agents are indifferent to the latency effects their choices cause for other users. Brandt and Weiss (2001) consider the implications of spitefulness in an auction setting (see also Liang and Qi (2007)). Kucuksenel (forthcoming) provides a broad analysis of the mechanism design prob- lem with other-regarding participants. In these papers and others (e.g., Levine (1998)), the established context is the non-regret-based altruism model wherein in- dividual utility is a linear combination of standard selfish utility and total social welfare, which we consider and move beyond in this paper. No previous work that we are aware of demonstrates the effect of limited altruism in yielding new positive mechanism design results; the introduction of our regret- based altruism model and such a demonstration are the main contributions of this paper. 1.2 Setup and mechanism design background There is a set of agents I = {1, 2,...,n} and a set of outcomes O. Each agent i ∈ I holds private information (or type) θi, an element of typespace Θi. A vector of agent types (a type profile) is θ =(θ1,...,θn) ∈ Θ1 × ... × Θn = Θ, and the same vector excluding the type of some agent i is denoted θ−i. A mechanism consists of a decision function f : Θ → O and transfer function vector T =(T1,...,Tn), with Ti :Θ → ℜ for each i ∈ I.