This paper provides an elementary, non-technical, survey of auction theory, by introducing and describing some of the critical papers in the subject. (The most important of these are reproduced in a companion book, The Economic Theory of Auctions, Paul Klemperer (ed.), Edward Elgar (pub.), forthcoming.) We begin with the most fundamental concepts, and then introduce the basic analysis of optimal auctions, the revenue equivalence theorem, and marginal revenues. Subsequent sections address risk-aversion, affiliation, asymmetries, entry, collusion, multi-unit auctions, double auctions, royalties, incentive contracts, and other topics. Appendices contain technical details, some simple worked examples, and a bibliography for each section.

This paper analyzes a class of games of incomplete information where each agent has

We analyze a market where (i) trade proceeds by random and anonymous pairwise meetings with bargaining; (ii) agents are asymmetrically informed about the value of the traded good; and (iii) no new entrants are allowed once the market is open. We show that information revelation and e±ciency never obtain in equilibrium, even as discounting is removed. This holds whether the asymmetry is two-sided or one-sided. In some cases there exist equilibria where a substantial amount goes untraded. This contrasts with the earlier literature, which was based on the steady-state equilibria of a model where agents enter the market every period.

We study a contest with multiple (not necessarily equal) prizes. Contestants have private information about an ability parameter that affects their costs of bidding. The contestant with the highest bid wins the first prize, the contestant with the second-highest bid wins the second prize, and so on until all the prizes are allocated. All contestants incur their respective costs of bidding. The contest’s designer maximizes the expected sum of bids. Our main results are: 1) We display bidding equlibria for any number of contestants having linear, convex or concave cost functions, and for any distribution of abilities. 2) If the cost functions are linear or concave, then, no matter what the distribution of abilities is, it is optimal for the designer to allocate the entire prize sum to a single ”first” prize. 3) We give a necessary and sufficient conditions ensuring that several prizes are optimal if contestants have a convex cost function.

This paper proposes an efficient agent for competing in Cliff Edge (CE) environments, such as sealed-bid auctions, dynamic pricing and the ultimatum game. The agent competes in one-shot CE interactions repeatedly, each time against a different human opponent, and its performance is evaluated based on all the interactions in which it participates. The agent, which learns the general pattern of the population’s behavior, does not apply any examples of previous interactions in the environment, neither of other competitors nor its own. We propose a generic approach which competes in different CE environments under the same configuration, with no knowledge about the specific rules of each environment. The underlying mechanism of the proposed agent is a new meta-algorithm, Deviated Virtual Learning (DVL), which extends existing methods to efficiently cope with environments comprising a large number of optional decisions at each decision point. Experiments comparing the performance of the proposed algorithm with algorithms taken from the literature, as well as another intuitive meta-algorithm, reveal a significant superiority of the former in average payoff and stability. In addition, the agent performed better than human competitors executing the same task.

We study all-pay auctions with variable rewards under incomplete information. In standard models, a reward depends on a bidder!s privately known type; however, in our model it is also a function of his bid. We show that in such models there is a potential for paradoxical behavior where a reduction in the rewards or an increase in costs may increase the expected sum of bids or alternatively the expected highest bid. Keywords: All-Pay Auctions, Contests, R & D Races, Rent-Seeking.

There are two well-studied timing games in economics: In a War of Attrition, more predecessors helps; in a pre-emption game, more predecessors hurts. This paper introduces and explores a new spanning class of timing games with rankorder payoffs that subsume both War of Attrition and Pre-emption Game as special cases, with endogenously-timed phase transition moments. Assuming unobserved actions and complete information, we identify equilibria that display both smooth and explosive entry — with a rich enough structure to capture a wider new array of economic and social timing phenomena. We prove existence, and then characterize the Nash equilibria, fleshing out the simple economics of phase transitions. We also bound the number of phase transitions using Karlin’s 1968 theory of total positivity, and describe the initial and terminal phases. We show that anticipation of later timing games influences current play — from swelling the magnitude of pre-emptive explosions to truncating wars of attrition. We conclude by a comparison with observable actions; while we find there a richer class of equilibria, we show how many of our insights do extend to this far more complicated environment.

This paper introduces an innovative approach for automated negotiating using the gender of human opponents. Our approach segments the information acquired from previous opponents, stores it in two databases, and models the typical behavior of males and of females. The two models are used in order to match an optimal strategy to each of the two subpopulations. In addition to the basic separation, we propose a learning algorithm which supplies an online indicator for the gender separability-level of the population, which tunes the level of separation the algorithm activates. The algorithm we present can be generally applied in different environments with no need for configuration of parameters. Experiments in 4 different one-shot domains, comparing the performance of the gender based separation approach with a basic approach which is not gender sensitive, revealed higher payoffs of the former in almost all the domains. Moreover, using the proposed learning algorithm further improved the results.

Preemption games are widely used to model patent races, innovation adoption and market entry problems. A previously neglected feature of these problems is that the agents ’ states (e.g. R&D …rms ’ technological improvements) are kept secret and stochastically change over time. We fully characterize equilibrium in preemption games where private information evolves according to Poisson processes, and provide a strategic rationale for the common wisdom that ‘big things happen fast. ’ In the context of patent races we surprisingly …nd that strengthening patent rights need not increase innovation disclosure. Furthermore, we clarify a basic welfare tradeo ¤ between duplication costs and preemption: the former likely take place in early stages of the race, and preemption in later stages.

I show that a unique equilibrium exists in an asymmetric two-player all-pay auction with a discrete signal structure that satisfies a monotonicity condition in each player’s signal. Independent signals and asymmetric interdependent valuations are a special case. The proof is constructive, and the construction is simple to implement as a computer program. For special cases, which include some private value settings, common value settings, and symmetric players, I derive additional properties and comparative statics. I also characterize the set of equilibria when a reserve price is introduced. 1