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Abstract:
The third generation UMTS auction in Germany raised an enormous amount of revenue, and at the same time achieved a more competitive market structure than other UMTS auctions in Europe. The present paper explains the design of that auction, and presents a game theoretic explanation of observed events during the crucial phase of that auction, which have puzzled several observers. In addition, the paper evaluates the merit of the German UMTS auction design, relative to the English design, that was predominantly employed in Europe.

Auctions, Telecommunications, Industrial Organization, Game Theory

Abstract:
This article studies the design of optimal mechanisms to regulate entry in natural oligopoly markets, assuming the regulator is unable to control the behavior of firms once they are in the market. We adapt the Clarke-Groves mechanism, characterize the optimal mechanism that maximizes the weighted sum of expected social surplus and expected tax revenue, and show that these mechanisms generally avoid budget deficits and prevent excessive entry.

Mechanism Design, Natural Oligopoly, Auctions, Entry

Abstract:
The second-generation GSM spectrum auction in Germany is probably the most clear cut example of a low price outcome in a simultaneous ascending-bid auction. The present paper gives an account of the events, describes the auction rules and market conditions, and provides a theoretical explanation of low price equilibria in simultaneous, ascending-bid auctions. In particular it is shown that the low price equilibrium that implements the efficient allocation is the unique perfect equilibrium of that game.

Multi-Unit Auctions, Spectrum Auctions, Telecommunications, Industrial Organization, Game Theory

Abstract:
In this paper, a notion of risk measure is defined for dynamic models. Three axioms, coherence, relevance and dynamic consistence, are postulated. It is shown that every dynamic risk measure that satisfies the axioms can be represented as the maximal expected present value of future losses where expectations are taken with respect to a set of probability measures. As new information arrives, this set of probability measures is updated in the Bayesian way. Moreover, dynamic consistency implies that this set satisfies a certain consistency condition.

Risk Measures, Consistency, Coherence, Dynamic Models

Abstract:
This paper develops a general theory of irreversible investment of a single firm that chooses a dynamic capacity expansion plan in an uncertain environment. The model is set up free of any distributional or any parametric assumptions and hence encompasses all the existing models. As the first contribution, a general existence and uniqueness result is provided for the optimal investment policy. Based upon an alternative approach developed previously to dynamic programming problems, we derive the optimal base capacity policy such that the firm always keeps the capacity at or above the base capacity. The critical base capacity is explicitly constructed and characterized via a stochastic backward equation. This method allows qualitative insights into the nature of the optimal investment under irreversibility. Finally, explicit solutions are derived for infinite time horizon, a separable operating profit function of Cobb--Douglas type and an exponential Levy process modelled economic shock.

Irreversible Investment, Capacity Expansion, Singular Control Problem, Levy Processes

Abstract:
The present note analyzes the Simultaneous Ascending Bid Auction with arbitrarily many bidders with decreasing marginal valuations under complete information. We show that the game is solvable by iterated elimination of weakly dominated strategies if the efficient allocation assigns at least one unit to every player and if bid increments are sufficiently small. In that unique equilibrium, bidders immediately reduce their demand to the efficient allocation, and the auction ends in the first round of bidding.

Multi-unit auctions

Abstract:
We consider optimal stopping problems for ambiguity averse decision makers with multiple priors. In general, backward induction fails. If, however, the class of priors is time-consistent, we establish a generalization of the classical theory of optimal stopping. To this end, we develop first steps of a martingale theory for multiple priors. We define minimax (super) martingales, provide a Doob-Meyer decomposition, and characterize minimax martingales. This allows us to extend the standard backward induction procedure to ambiguous, time'consistent preferences. The value function is the smallest process that is a minimax supermartingale and dominates the payoff process. It is optimal to stop when the current payoff is equal to the value function. Moving on, we study the infinite horizon case. We show that the value process satisfies the same backward recursion (Bellman equation) as in the finite horizon case. The finite horizon solutions converge to the infinite horizon solution. Finally, we characterize completely the set of time-consistent multiple priors in the binomial tree. We solve two classes of examples: the so-called independent and indistinguishable case (the parking problem) and the case of American Options (Cox-Ross-Rubinstein model).

Optimal Stopping, Ambiguity, Uncertainty Aversion, American Options

Abstract:
Experimental evidence stresses the importance of so-called social preferences for understanding economic behavior. Social preferences are defined over the entire allocation in a given economic environment, and not just over one's own consumption as is traditionally presumed. We study the implications for competitive market outcomes if agents have such preferences. First, we clarify under what conditions an agent behaves as if she was selfish — i.e. when her demand function is independent of others' behavior. An agent behaves as if selfish if and only if her preferences can be represented by a utility function that is separable between her own utility and the allocation of goods for all other agents. Next, we study equilibrium outcomes in economies where individual agents behave as if selfish. We show that one can identify a corresponding ego-economy such that the equilibria of the ego-economy coincide with the equilibria of the original economy. As a consequence, competitive equilibria exist and they are material efficient. In general, however, the First Welfare Theorem fails. We introduce the class of Bergsonian social utility functions, which are social utility functions that are completely separable in all agents' material utility. For such social preferences, the Second Welfare Theorem holds under a suitable growth condition. We also establish that in uncertain environments, agents with social preferences typically do not behave as if selfish. Furthermore, in the presence of public goods, both demand and equilibrium outcomes depend on social preferences.

General Equilibrium, Social Preferences, Welfare, Externalities

Abstract:
Brown and von Neumann introduced a dynamical system that converges to saddle points of zero sum games with finitely many strategies. Nash used the mapping underlying these dynamics to prove existence of equilibria in general games. The resulting Brown--von Neumann--Nash dynamics are a benchmark example for myopic adjustment dynamics that, in contrast to replicator dynamics, allow for innovation, but require less rationality than the best response dynamics. This paper studies the BNN dynamics for games with infinitely many strategies. We establish Nash stationarity for continuous payoff functions. For negative semidefinite games (that include zero sum games), we generalize the results of Brown and von Neumann. In addition, we show that evolutionarily robust Nash equilibria are asymptotically stable. A complete stability analysis for doubly symmetric games is also obtained.

learning in games, evolutionary stability, BNN

Abstract:
The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this unsatisfying restriction is unnecessary. We specify a simple condition under which the continuous time replicator dynamics are well defined for the case of infinite strategy spaces. Furthermore, we provide new conditions for the stability of rest points and show that even strict equilibria may be unstable. Finally, we apply this general theory to a number of applications like the Nash demand game, the War of Attrition, linear-quadratic games, the harvest preemption game, and games with mixed strategies.

Keywords and Phrases: Replicator dynamics, Evolutionary stability, Continuous strategy spaces.

Abstract:
The effect of incomplete information on the term structure of interest rates is examined in the framework of a pure exchange economy under uncertainty where aggregate output grows at a constant rate. If the growth rate is known, the term structure is flat. In contrast, the term structure is a decreasing curve when agents do not know the growth rate. Long term yields are less than the short rate and the yield of long term bonds is determined by the worst possible realizations of future short rates.

Incomplete information, term structure of interest rates