The Combinatorial World (of Auctions) According to GARP

Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function

Taxation of Asset Income in the Presence of a World Securites Market

This paper shows, using a standard CAPM model of security prices in a world market, that even small countries can affect the price of domestically issued risky securities, while large countries can affect the prices of all securities. As a result, countries have the incentive to set tax rates such that in equilibrium investors specialize in domestic securities, and net capital flows between countries are restricted. Each country does this to increase the utility of domestic residents, taking as given the tax policies of other governments, but the net outcome is a reduction in world efficiency and likely a reduction in the utility of all individuals.

The Attack-and-Defense Group Contests: Best-shot versus Weakest-link

This study analyzes a group contest in which one group (defenders) follows a weakest-link whereas the other group (attackers) follows a best-shot impact function. We fully characterize the Nash and coalition-proof equilibria and show that with symmetric valuation the coalition-proof equilibrium is unique up to the permutation of the identity of the active player in the attacker group. With asymmetric valuation it is always an equilibrium for one of the highest valuation players to be active; it may also be the case that the highest valuation players in the attacker group free-ride completely on a group-member with a lower valuation. However, in any equilibrium, only one player in the attacker group is active, whereas all the players in the defender group are active and exert the same effort. We also characterize the Nash and coalition-proof equilibria for the case in which one group follows either a best-shot or a weakest-link but the other group follows an additive impact function

A Typology of Corrupt Transactions in Developing Countries

Summary Economic theory has attempted to identify the conditions under which corruption has particularly harmful effects. This article evaluates these theories and argues that the classifications offered are misleading. Very successful interventionist states have suffered from corruption just as much as very unsuccessful ones. Policy responses to corruption require an understanding of the effects of corruption and the determinants of these effects. The fact which appears to have a strong effect in determining the harmfulness of corruption is the balance of power between the state and its clients. An alternative classification of the effects of corruption is suggested on this basis

Price competition with consumer confusion

Copyright © 2013, INFORMS. Article posted with permission.This paper proposes a model in which identical sellers of a homogeneous product compete in both prices and price frames (i.e., ways to present price information). Frame choices affect the comparability of price offers and may cause consumer confusion and lower price sensitivity. In equilibrium, firms randomize their frame choices to obfuscate price comparisons and sustain positive profits. The nature of the equilibrium depends on whether frame differentiation or frame complexity is more confusing. Moreover, an increase in the number of competitors induces firms to rely more on frame complexity, and this may boost industry profits and lower consumer surplus

Intergenerational Risk Sharing

In this paper we examine government debt and tax-transfer policies that can improve the allocation of risk between generations. Markets cannot allocate risk efficiently between two generations whenever the two generations are not both alive prior to the occurrence of a stochastic event. This implies that government policies transferring risk between generations have the potential to create first-order welfare improvements. Our model provides a non-Keynesian justification for debt-finance of wars and recessions, as well as an added rationale for Social Security type tax-transfer schemes which aid unlucky generations, e.g., the Depression generation, at the expense of luckier generations.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100725/1/ECON193.pd

Taxation of Asset Income in the Presence of a World Securities Market

This paper shows, using a standard CAPM model of security prices in a world market, that even small countries can affect the price of domestically issued risky securities, while large countries can affect the prices of all securities. As a result, countries have the incentive to set tax rates such that in equilibrium investors tend to specialize in domestic securities, and net capital flows between countries are restricted. Each country does this to increase the utility of domestic residents, taking as given the tax policies of other governments, but the net outcome is a reduction in world efficiency and likely a reduction in the utility of all investors.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100727/1/ECON195.pd

Strategy bifurcation and spatial inhomogeneity in a simple model of competing sellers

We present a simple one-parameter model for spatially localised evolving agents competing for spatially localised resources. The model considers selling agents able to evolve their pricing strategy in competition for a fixed market. Despite its simplicity, the model displays extraordinarily rich behavior. In addition to ``cheap'' sellers pricing to cover their costs, ``expensive'' sellers spontaneously appear to exploit short-term favorable situations. These expensive sellers ``speciate'' into discrete price bands. As well as variety in pricing strategy, the ``cheap'' sellers evolve a strongly correlated spatial structure, which in turn creates niches for their expensive competitors. Thus an entire ecosystem of coexisting, discrete, symmetry-breaking strategies arises.Comment: 6 pages, 6 figures, epl2; 1 new figure, include nash equilibrium analysis, typo fixe

Testing Consumer Rationality using Perfect Graphs and Oriented Discs

Given a consumer data-set, the axioms of revealed preference proffer a binary test for rational behaviour. A natural (non-binary) measure of the degree of rationality exhibited by the consumer is the minimum number of data points whose removal induces a rationalisable data-set.We study the computational complexity of the resultant consumer rationality problem in this paper. This problem is, in the worst case, equivalent (in terms of approximation) to the directed feedback vertex set problem. Our main result is to obtain an exact threshold on the number of commodities that separates easy cases and hard cases. Specifically, for two-commodity markets the consumer rationality problem is polynomial time solvable; we prove this via a reduction to the vertex cover problem on perfect graphs. For three-commodity markets, however, the problem is NP-complete; we prove thisusing a reduction from planar 3-SAT that is based upon oriented-disc drawings

Competitive market for multiple firms and economic crisis

The origin of economic crises is a key problem for economics. We present a model of long-run competitive markets to show that the multiplicity of behaviors in an economic system, over a long time scale, emerge as statistical regularities (perfectly competitive markets obey Bose-Einstein statistics and purely monopolistic-competitive markets obey Boltzmann statistics) and that how interaction among firms influences the evolutionary of competitive markets. It has been widely accepted that perfect competition is most efficient. Our study shows that the perfectly competitive system, as an extreme case of competitive markets, is most efficient but not stable, and gives rise to economic crises as society reaches full employment. In the economic crisis revealed by our model, many firms condense (collapse) into the lowest supply level (zero supply, namely bankruptcy status), in analogy to Bose-Einstein condensation. This curious phenomenon arises because perfect competition (homogeneous competitions) equals symmetric (indistinguishable) investment direction, a fact abhorred by nature. Therefore, we urge the promotion of monopolistic competition (heterogeneous competitions) rather than perfect competition. To provide early warning of economic crises, we introduce a resolving index of investment, which approaches zero in the run-up to an economic crisis. On the other hand, our model discloses, as a profound conclusion, that the technological level for a long-run social or economic system is proportional to the freedom (disorder) of this system; in other words, technology equals the entropy of system. As an application of this new concept, we give a possible answer to the Needham question: "Why was it that despite the immense achievements of traditional China it had been in Europe and not in China that the scientific and industrial revolutions occurred?"Comment: 17 pages; 3 figure