Continuous-time games of timing

We address the question of existence of equilibrium in general timing games with complete information. Under weak assumptions, any two-player timing game has a Markov subgame perfect -equilibrium, for each >0. This result is tight. For some classes of games (symmetric games, games with cumulative payoffs), stronger existence results are established.     

Methods for estimating optimal Dickson and Waters modification dividend barrier

In applications of collective risk theory, complete information for the distribution of individual claims amount is often unknown, but reliable estimates of its first few moments may be available. Dickson and Waters [Dickson, D.C.M. and Waters, H.R., (2004) Some optimal dividends problems, Astin Bulletin, 34, 49–74.] pointed out that shareholders should be liable to cover the deficit at ruin. Thus, they considered b the level of the barrier that maximizes the expectation of the difference between the discounted dividends until ruin and the discounted deficit at ruin. For such a situation, this paper develops methods for estimating the Dickson–Waters modification for the optimal dividend barrier b with the expectation of discounted penalty at ruin. In particular, two De Vylder approximations are explained, and the diffusion approximation for the expectation of discounted penalty at ruin is examined. For several claim amount distributions, the approximate values are compared numerically with exact values.     

Attitude toward imprecise information

This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to take the form of a probability–possibility set, that is, a set P of probability measures on the state space. The decision maker is told that the true probability law lies in P and is assumed to rank pairs of the form (P,f) where f is an act mapping states into outcomes. The key representation result delivers maxmin expected utility (MEU) where the min operator ranges over a set of probability priors—just as in the MEU representation result of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141–153]. However, unlike the MEU representation, the representation here also delivers a mapping, , which links the probability–possibility set, describing the available information, to the set of revealed priors. The mapping is shown to represent the decision maker's attitude to imprecise information: under our axioms, the set of representation priors is constituted as a selection from the probability–possibility set. This allows both expected utility when the selected set is a singleton and extreme pessimism when the selected set is the same as the probability–possibility set, i.e., is the identity mapping. We define a notion of comparative imprecision aversion and show it is characterized by inclusion of the sets of revealed probability distributions, irrespective of the utility functions that capture risk attitude. We also identify an explicit attitude toward imprecision that underlies usual hedging axioms. Finally, we characterize, under extra axioms, a more specific functional form, in which the set of selected probability distributions is obtained by (i) solving for the “mean value” of the probability–possibility set, and (ii) shrinking the probability–possibility set toward the mean value to a degree determined by preferences.     

Almost budget-balanced VCG mechanisms to assign multiple objects

Subsidy-free VCG mechanisms assign p identical objects to n agents. The efficiency loss is the largest ratio of budget surplus to efficient surplus, over all profiles of non-negative valuations. The smallest efficiency loss satisfies . If is bounded away from , converges to zero exponentially in n.Participation is voluntary in the optimal mechanism achieving if p=1, but not if p?2. Among voluntary mechanisms, the optimal efficiency loss is not significantly larger than if . But it does not converge to zero in n if .     

Poverty trap and global indeterminacy in a growth model with open-access natural resources

In this paper we use global analysis techniques to analyze an economic growth model with environmental negative externalities, giving rise to a three-dimensional dynamic system (the framework is the one introduced by Wirl (1997) [53]). The dynamics of our model admits a locally attracting stationary state , which is, in fact, a poverty trap, coexisting with another stationary state possessing saddle-point stability. Global dynamical analysis shows that, under some conditions on the parameters, if the initial values of the state variables are close enough to the coordinates of , then there exists a continuum of equilibrium trajectories approaching and one trajectory approaching . Therefore, our model exhibits global indeterminacy, since either or can be selected according to agent expectations. Moreover, we prove that conditions guaranteeing the attractivity of also imply the saddle-point stability of . However, when is not attractive, numerical simulations show the possible existence of one or two limit cycles: an attractive one surrounding and one endowed with a two-dimensional stable manifold surrounding .     

New complexity results about Nash equilibria

We provide a single reduction that demonstrates that in normal-form games: (1) it is -complete to determine whether Nash equilibria with certain natural properties exist (these results are similar to those obtained by Gilboa and Zemel [Gilboa, I., Zemel, E., 1989. Nash and correlated equilibria: Some complexity considerations. Games Econ. Behav. 1, 80–93]), (2) more significantly, the problems of maximizing certain properties of a Nash equilibrium are inapproximable (unless ), and (3) it is -hard to count the Nash equilibria. We also show that determining whether a pure-strategy Bayes–Nash equilibrium exists in a Bayesian game is -complete, and that determining whether a pure-strategy Nash equilibrium exists in a Markov (stochastic) game is -hard even if the game is unobserved (and that this remains -hard if the game has finite length). All of our hardness results hold even if there are only two players and the game is symmetric.     

Absorbing Team Games

A team is a group of people having the same motives but possibly different available actions. A team game is a game where two teams face each other. An absorbing game is a repeated game where some of the entries are absorbing, in the sense that once they are chosen the play terminates, and all future payoffs are equal to the payoff at the stage of termination. We prove that every absorbing team game has an equilibrium payoff and that there are -equilibrium profiles with cyclic structure. Journal of Economic Literature Classification Numbers: C72, C73.     

Local financial benefits of rain forests: comparative evidence from Amerindian societies in Bolivia and Honduras

Researchers generally express the local value of tropical rain forests in dollars/ha/year. The approach is problematic because it produces low values to local users, underestimating the importance of the forest expressed as a share of household consumption or earnings. Here we contribute to valuation studies of rain forests by estimating the financial importance of the forest measured in three ways: (1) the contribution of forests to annual household consumption and (2) earnings; and (3) the value of a hectare of rain forest to villagers measured through the biological goods consumed and sold. We collected panel data on consumption and earnings from 81 households in four villages of two Amerindian societies in two nations (Tsimane’, Bolivia; Tawahka, Honduras). Analyses suggest: (1) forests account for a large share of household consumption (median 38.5%; range 14.65–53.11%); (2) forests contribute more to household consumption than to household earnings (median 22.69%; range 16.56–44.81%); (3) the relative contribution of forests to household consumption and earnings falls among villages closer to towns; and (4) the range of values/year of rain forest/ha is US$7.10–9.70 using 1999 dollars or US$18.46–46.56 using purchasing power parity indexes, below previous estimates. Results show much variation in forest values; valuation methods and stakeholder perspectives affect the variation. Given the variation, a useful strategy to promote forest conservation would transfer income to villagers to compensate them for non-local forest values.     

Apportioning of risks via stochastic dominance

Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable dominates via ith-order stochastic dominance for i=M,N. We show that the 50-50 lottery dominates the lottery via (N+M)th-order stochastic dominance. The basic idea is that a decision maker exhibiting (N+M)th-order stochastic dominance preference will allocate the state-contingent lotteries in such a way as not to group the two “bad” lotteries in the same state, where “bad” is defined via ith-order stochastic dominance. In this way, we can extend and generalize existing results about risk attitudes. This lottery preference includes behavior exhibiting higher-order risk effects, such as precautionary effects and tempering effects.     

Set-rationalizable choice and self-stability

Rationalizability and similar notions of consistency have proved to be highly problematic in the context of social choice, as witnessed by a range of impossibility results, among which Arrow?s is the most prominent. We propose to rationalize choice functions by preference relations over sets of alternatives (set-rationalizability) and introduce two consistency conditions, and , which are defined in analogy to Sen?s α and γ. We find that a choice function satisfies if and only if it is set-rationalizable and that it satisfies and if and only if it is self-stable, a new concept based on earlier work by Dutta. The class of self-stable social choice functions contains a number of appealing Condorcet extensions.     

Benchmarking real-valued acts

A benchmarking procedure ranks real-valued acts by the probability that they outperform a benchmark β which may itself be a random variable; that is, an act f is evaluated by means of the functional V(f)=P(fβ). Expected utility is a special case of benchmarking procedure, where the acts and the benchmark are stochastically independent. This paper provides axiomatic characterizations of preference relations that are representable as benchmarking procedures. The key axiom is the sure-thing principle. When the state space is infinite, different continuity assumptions translate into different properties of the probability P.     

Monotonic and implementable solutions in generalized matching problems

We consider one-to-one matching problems when preferences are weak orders and search for (Maskin-)monotonic and implementable solutions. We show that for any coalition structure , the strong -core is monotonic if and only if it is the individually rational solution. We introduce a solution, which we call the “union strong -core”, and show that this solution is the minimal way to expand the strong -core recovering monotonicity. We also show that the union strong -core is implementable.     

Farsightedly stable networks

A set of networks G is pairwise farsightedly stable (i) if all possible farsighted pairwise deviations from any network g G to a network outside G are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying conditions (i) and (ii). A non-empty pairwise farsightedly stable set always exists. We provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsighted stability yields a Pareto dominant network, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest pairwise consistent set and the von Neumann–Morgenstern pairwise farsightedly stable set.     

Buy-price English auction

Consider an English auction for a single object in which there is an option for a bidder to guarantee a purchase at a seller-specified buy price b at any time. We show that there exist and (), such that a bidder purchases at the buy price immediately if his valuation v is no less than or and at least one other bidder is participating in the auction. If , he purchases at the buy price once the current bid reaches a strategically chosen threshold price. A properly set buy price increases expected social welfare and the expected utility of each agent when either buyers or seller are risk-averse.     

Existence of adaptively stable sunspot equilibria near an indeterminate steady state

We examine the nonlinear model x_t=E_tF(x_t+1). Markov stationary sunspot equilibria (SSEs) exist near an indeterminate steady state, , provided . Despite the importance of indeterminacy in macroeconomics, earlier results have not provided conditions for the existence of adaptively stable SSEs near an indeterminate steady state. We show that there exist Markov SSEs near x? that are E-stable, and therefore locally stable under adaptive learning, if .     

Contests with a stochastic number of players

We study Tullock's (1980) n-player contest when each player has an independent probability 0 < p 1 of participating. A unique symmetric equilibrium is found for any n and p and its properties are analyzed. In particular, we show that for a fixed n > 2 individual equilibrium spending as a function of p is single-peaked and satisfies a single-crossing property for any two different numbers of potential players. However, total equilibrium spending is monotonically increasing in p and n. We also demonstrate that ex-post over-dissipation is a feature of the pure-strategy equilibrium in our model. It turns out that if the contest designer can strategically decide whether to reveal the actual number of participating players or not, then the actual number of participants is always revealed.     

Duality of welfare and profit maximization

Many economists are aware that the conditions for the efficiency and monopolization in a partial equilibrium framework are the extremes of the Ramsey–Boiteux formula when the Lagrange multiplier for the budget varies. We formalize the duality existing between the welfarist and monopolist constrained maximization programs by proving the following “folk theorem”:      

Foundations of neo-Bayesian statistics

We study an axiomatic model of preferences, which contains as special cases Subjective Expected Utility, Choquet Expected Utility, Maxmin and Maxmax Expected Utility and many other models. First, we give a complete characterization of the class of functionals representing these preferences. Then, we show that any such functional can be represented as a Choquet integral

where is the canonical mapping from the space of bounded Σ-measurable functions into the space of weak^*-continuous affine functions on a weak*-compact, convex set of probability measures on Σ. Conversely, any preference relation defined by means of such functionals satisfies the axioms of the model we study. Different properties of the capacity give rise to different models. Our result shows that the idea of Choquet integration is general enough to embrace all the models mentioned above. In doing so, it widens the range of applicability of well-known procedures in robust statistics theory such as the Neyman–Pearson lemma for capacities [P.J. Huber, V. Strassen, Minimax tests and the Neyman–Pearson lemma for capacities, Ann. Statist. 1 (1973) 251–263], Bayes' theorem for capacities [J.B. Kadane, L. Wasserman, Bayes' theorem for Choquet capacities, Ann. Statist. 18 (1990) 1328–1339] or of results like the Law of Large numbers for capacities [F. Maccheroni, M. Marinacci, A strong law of large numbers for capacities, Ann. Probab. 33 (2005) 1171–1178].     

From “tax state” to “debt state”

The paper is motivated by Joseph A. Schumpeter's The Crisis of the Tax State. It inquires whether the buildup of government debt in peacetimeprosperity is a threat to the stability, existence or creation of viable tax states. The paper begins by setting out Schumpeter's conception of the tax state and the nature of recent political-economic events which have reinvigorated the concept. Next the paper sets out some simple debt dynamics and sketches a debt-induced business cycle arising from heavy reliance on debt finance in peacetimeprosperity. Finally, the paper assesses threats to the tax state in light of recent work on path dependence and positive feedback. An attempt is made to throw some light on whether the plethora of new, and often small, states spawned by the demise of communism can be viable tax states.Essay on Government, the Tax State and Economic Dynamics submitted to the Third Schumpeter Prize Competition.     

The impact of minimum wages on youth employment in Portugal

On January 1, 1987, the legal minimum wage for workers aged 18 and 19 in Portugal was raised by 49.3%. This shock is used as a “natural experiment” to evaluate the impact of the minimum wage change on teenagers’ employment. The method is to compare, based on firm-level microdata, the employment growth of 18-19-year-old workers with employment growth of older workers. The main findings are that the increase in the minimum wage significantly reduced employment of 18 and olds, but increased employment of 20- olds.