Paul Schweinzer

The roles of stories in applying game theory

Game‐theoretic models consist of a formal game structure and an informal model narrative or story. When game theory is employed to model economic situations, the stories play a central role in interpreting, constructing and solving game structures. We analyse the architecture of game theory and distinguish between game models and the theory proper. We present the different functions of the model narrative in the application of game models to economic situations. In particular, we show how model narratives support the choice of solution concepts defined and provided by the theory proper. We further argue that the narratives role in interpretation, construction and solution makes it a necessary part of a game model that is intended to be a model of an economic situation. We conclude that game theory is not a universal theory of rationality, but only offers tools to model specific situations at varying degrees and kinds of rationality.

The optimal prize structure of symmetric Tullock contests

We show that the optimal prize structure of symmetric n-player Tullock tournaments assigns the entire prize pool to the winner, provided that a symmetric pure strategy equilibrium exists. If such an equilibrium fails to exist under the winner-take-all structure, we construct the optimal prize structure which improves existence conditions by dampening efforts. If no such optimal equilibrium exists, no symmetric pure strategy equilibrium induces positive efforts.

Efficient Tournaments within Teams

We analyze incentive problems in team and partnership structures where the only available information to condition a contract on is a partial and noisy ranking which specifies who comes first in efforts among the competing partners. This enables us to ensure both first-best efficient effort levels for all partners and the redistribution of output only among partners. Our efficiency result is obtained for a wide range of cost and production functions. Copyright (c) 2009, RAND.

When Queueing is Better than Push and Shove

We address the scheduling problem of reordering an existing queue into its efficient order through trade. To that end, we consider individually rational and balanced budget direct and indirect mechanisms. We show that this class of mechanisms allows us to form efficient queues provided that existing property rights for the service are small enough to enable trade between the agents. In particular, we show on the one hand that no queue under a fully deterministic service schedule such as first-come, first-serve can be dissolved efficiently and meet our requirements. If, on the other hand, the alternative is service anarchy (ie. a random queue), every existing queue can be transformed into an efficient order.

Efficient Emissions Reduction

We propose a simple mechanism providing incentives to reduce harmful emissions to their efficient level without infracting upon productive efficiency. I t employs a contest creating incentives among participating nations to simultaneously exert efficient productive and efficient abatement efforts. Participation in the most stylised form of the scheme is voluntary and individually rational. All rules are mutually agreeable and are unanimously adopted if proposed. The scheme balances its budget and requires no principal. The mechanism provides a benchmark result for the cost of the implementation of these desirable properties. In a more realistic setup which could potentially inform policy decisions, we discuss participation enforcement through punishment clauses, exclusive trade agreements, and environmental standards as effective means to discourage free-riding. (JEL C7, D7, H4, Q5. Keywords: Climate policy, Contests, Efficiency.)

Auctioning Risk: The All-Pay Auction under Mean-Variance Preferences

We analyse the all-pay auction with incomplete information and variance-averse bidders. We characterise the unique symmetric equilibrium for general distributions of valuations and any number of bidders. Variance aversion is a sufficient assumption to predict that high-valuation bidders increase their bids relative to the risk-neutral case while low types decrease their bid. Considering an asymmetric two-player environment with uniformly distributed valuations, we show that a variance-averse player always bids higher than her risk-neutral opponent with the same valuation. Utilising our analytically derived bidding functions we discuss all-pay auctions with variance-averse bidders from an auction designer’s perspective. We briefly consider possible extensions of our model, including noisy signals, type-dependent attitudes towards risk, and variance-seeking preferences.

Labour market recruiting with intermediaries

We consider a Rothschild-Stiglitz-Spence labour market model and employ a centralised mechanism to coordinate the efficient matching of workers to firms. This mechanism can be thought of as operated by a recruitment agency, an employment office or head hunter. In a centralised descending-bid, multi-item procurement auction, workers submit wage-bids for each job and are assigned stable jobs as equilibrium outcome. We compare this outcome to independent, sequential hiring by firms and conclude that, in general, a stable assignment can only be implemented if firms coordinate to some extent. (JEL C78, D44, E24, J41. Keywords: Matching, Multi-item auctions, Sequential auctions.)

How to share it out: The value of information in teams ☆

We study the role of information exchange, leadership, and coordination in team and partnership structures. For this purpose, we view individuals jointly engaging in productive processes—a “team”—as endowed with individual and privately held information on the joint production process. Once each team member decides on whether or not to share his private information truthfully, he chooses which effort to exert in the joint production process. This effort, however, is not contractible: only the realized output (or profit) of the team can be observed. Our central question is whether or not incentives can be provided to a team in this environment such that team members communicate their private information and exert efficient productive efforts on the basis of this communication. Our main result shows that there exists a simple ranking-based contract that implements both desiderata in a wide set of situations.

Agreeing on Efficient Emissions Reduction

We propose a simple mechanism providing incentives to reduce harmful emissions to their efficient level without infracting upon productive efficiency. The mechanism employs a contest creating incentives among participating nations to simultaneously exert efficient productive and efficient abatement efforts. Participation in the most stylised form of the scheme is voluntary and individually rational; all rules are mutually agreeable and are unanimously adopted if proposed. The scheme balances its budget and requires no principal. In a perhaps more realistic stochastic output version which could potentially inform policy decisions, we show that the transfers required by the efficient mechanism create a mutual insurance motive which may serve as effective rationale for the (gradual) formation of International Environmental Agreements.