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We study competition among contests in a general model that allows for an arbitrary and heterogeneous space of contest design, where the goal of the contest designers is to maximize the contestants sum of efforts. Our main result shows that optimal contests in the monopolistic setting (i.e., those that maximize the sum of efforts in a model with a single contest) form an equilibrium in the model with competition among contests. Under a very natural assumption these contests are in fact dominant, and the equilibria that they form are unique. Moreover, equilibria with the optimal contests are Pareto-optimal even in cases where other equilibria emerge. In many natural cases, they also maximize the social welfare.
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Incentives are more likely to elicit desired outcomes when they are designed based on accurate models of agents strategic behavior. A growing literature, however, suggests that people do not quite behave like standard economic agents in a variety of environments, both online and offline. What consequences might such differences have for the optimal design of mechanisms in these environments? In this paper, we explore this question in the context of optimal contest design for simple agents---agents who strategically reason about whether or not to participate in a system, but not about the input they provide to it. Specifically, consider a contest where $n$ potential contestants with types $(q_i,c_i)$ each choose between participating and producing a submission of quality $q_i$ at cost $c_i$, versus not participating at all, to maximize their utilities. How should a principal distribute a total prize $V$ amongst the $n$ ranks to maximize some increasing function of the qualities of elicited submissions in a contest with such simple agents? We first solve the optimal contest design problem for settings with homogenous participation costs $c_i = c$. Here, the optimal contest is always a simple contest, awarding equal prizes to the top $j^*$ contestants for a suitable choice of $j^*$. (In comparable models with strategic effort choices, the optimal contest is either a winner-take-all contest or awards possibly unequal prizes, depending on the curvature of agents effort cost functions.) We next address the general case with heterogeneous costs where agents types are inherently two-dimensional, significantly complicating equilibrium analysis. Our main result here is that the winner-take-all contest is a 3-approximation of the optimal contest when the principals objective is to maximize the quality of the best elicited contribution.
When selling information products, the seller can provide some free partial information to change peoples valuations so that the overall revenue can possibly be increased. We study the general problem of advertising information products by revealing partial information. We consider buyers who are decision-makers. The outcomes of the decision problems depend on the state of the world that is unknown to the buyers. The buyers can make their own observations and thus can hold different personal beliefs about the state of the world. There is an information seller who has access to the state of the world. The seller can promote the information by revealing some partial information. We assume that the seller chooses a long-term advertising strategy and then commits to it. The sellers goal is to maximize the expected revenue. We study the problem in two settings. (1) The seller targets buyers of a certain type. In this case, we prove that finding the optimal advertising strategy is equivalent to finding the concave closure of a simple function. The function is a product of two quantities, the likelihood ratio and the cost of uncertainty. Based on this observation, we prove some properties of the optimal mechanism, which allow us to solve for the optimal mechanism by a finite-size convex program. The convex program will have a polynomial size if the state of the world has a constant number of possible realizations or the buyers face a decision problem with a constant number of options. For the general problem, we prove that it is NP-hard to find the optimal mechanism. (2) When the seller faces buyers of different types and only knows the distribution of their types, we provide an approximation algorithm when it is not too hard to predict the possible type of buyers who will make the purchase. For the general problem, we prove that it is NP-hard to find a constant-factor approximation.
We identify the first static credible mechanism for multi-item additive auctions that achieves a constant factor of the optimal revenue. This is one instance of a more general framework for designing two-part tariff auctions, adapting the duality framework of Cai et al [CDW16]. Given a (not necessarily incentive compatible) auction format $A$ satisfying certain technical conditions, our framework augments the auction with a personalized entry fee for each bidder, which must be paid before the auction can be accessed. These entry fees depend only on the prior distribution of bidder types, and in particular are independent of realized bids. Our framework can be used with many common auction formats, such as simultaneous first-price, simultaneous second-price, and simultaneous all-pay auctions. If all-pay auctions are used, we prove that the resulting mechanism is credible in the sense that the auctioneer cannot benefit by deviating from the stated mechanism after observing agent bids. If second-price auctions are used, we obtain a truthful $O(1)$-approximate mechanism with fixed entry fees that are amenable to tuning via online learning techniques. Our results for first price and all-pay are the first revenue guarantees of non-truthful mechanisms in multi-dimensional environments; an open question in the literature [RST17].
The Competition Complexity of an auction setting refers to the number of additional bidders necessary in order for the (deterministic, prior-independent, dominant strategy truthful) Vickrey-Clarke-Groves mechanism to achieve greater revenue than the (randomized, prior-dependent, Bayesian-truthful) optimal mechanism without the additional bidders. We prove that the competition complexity of $n$ bidders with additive valuations over $m$ independent items is at most $n(ln(1+m/n)+2)$, and also at most $9sqrt{nm}$. When $n leq m$, the first bound is optimal up to constant factors, even when the items are i.i.d. and regular. When $n geq m$, the second bound is optimal for the benchmark introduced in [EFFTW17a] up to constant factors, even when the items are i.i.d. and regular. We further show that, while the Eden et al. benchmark is not necessarily tight in the $n geq m$ regime, the competition complexity of $n$ bidders with additive valuations over even $2$ i.i.d. regular items is indeed $omega(1)$. Our main technical contribution is a reduction from analyzing the Eden et al. benchmark to proving stochastic dominance of certain random variables.
Incentive mechanisms for crowdsourcing have been extensively studied under the framework of all-pay auctions. Along a distinct line, this paper proposes to use Tullock contests as an alternative tool to design incentive mechanisms for crowdsourcing. We are inspired by the conduciveness of Tullock contests to attracting user entry (yet not necessarily a higher revenue) in other domains. In this paper, we explore a new dimension in optimal Tullock contest design, by superseding the contest prize---which is fixed in conventional Tullock contests---with a prize function that is dependent on the (unknown) winners contribution, in order to maximize the crowdsourcers utility. We show that this approach leads to attractive practical advantages: (a) it is well-suited for rapid prototyping in fully distributed web agents and smartphone apps; (b) it overcomes the disincentive to participate caused by players antagonism to an increasing number of rivals. Furthermore, we optimize conventional, fixed-prize Tullock contests to construct the most superior benchmark to compare against our mechanism. Through extensive evaluations, we show that our mechanism significantly outperforms the optimal benchmark, by over three folds on the crowdsourcers utility cum profit and up to nine folds on the players social welfare.
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