Economics

We propose six axioms concerning when one candidate should defeat another in a democratic election involving two or more candidates. Five of the axioms are widely satisfied by known voting procedures. The sixth axiom is a weakening of Kenneth Arrow's famous condition of the Independence of Irrelevant Alternatives (IIA). We call this weakening Coherent IIA. We prove that the five axioms plus Coherent IIA single out a voting procedure studied in our recent work: Split Cycle. In particular, Split Cycle is the most resolute voting procedure satisfying the six axioms for democratic defeat. In addition, we analyze how Split Cycle escapes Arrow's Impossibility Theorem and related impossibility results.

We show that under plausible levels of background risk, no theory of choice under risk -- such as expected utility theory, prospect theory, or rank dependent utility -- can simultaneously satisfy the following three economic postulates: (i) Decision makers are risk-averse over small gambles, (ii) they respect stochastic dominance, and (iii) they account for background risk.

The purpose is to compare the perfect Stochastic Return (SR) model like Islamic banks to the Fixed Return (FR) model as in conventional banks by measuring up their impacts at the macroeconomic level. We prove that if the optimal choice of investor share in SR model {\alpha}* realizes the indifference of the financial institution toward SR and FR models, there exists {\alpha} less than {\alpha}* such that the banks strictly prefers the SR model. Also, there exists {\alpha}, {\gamma} and {\lambda} verifying the conditions of {\alpha}-sharing such that each party in economy can be better under the SR model and the economic welfare could be improved in a Pareto-efficient way.

How can a receiver design an information structure in order to elicit information from a sender? We study how a decision-maker can acquire more information from an agent by reducing her own ability to observe what the agent transmits. Intuitively, when the two parties' preferences are not perfectly aligned, this garbling relaxes the sender's concern that the receiver will use her information to the sender's disadvantage. We characterize the optimal information structure for the receiver. The main result is that under broad conditions, the receiver can do just as well as if she could commit to a rule mapping the sender's message to actions: information design is just as good as full commitment. Similarly, we show that these conditions guarantee that ex ante information acquisition always benefits the receiver, even though this learning might actually lower the receiver's expected payoff in the absence of garbling. We illustrate these effects in a range of economically relevant examples.

We consider a discrete-time nonatomic routing game with variable demand and uncertain costs. Given a routing network with single origin and destination, the cost function of each edge depends on some uncertain persistent state parameter. At every period, a random traffc demand is routed through the network according to a Bayes-Wardrop equilibrium. The realized costs are publicly observed and the Bayesian belief about the state parameter is updated. We say that there is strong learning when beliefs converge to the truth and weak learning when the equilibrium flow converges to the complete-information flow. We characterize the networks for which learning occurs. We prove that these networks have a series-parallel structure and provide a counterexample to prove that the condition is necessary.

This paper brings together divergent approaches to time inconsistency from macroeconomic policy and behavioural economics. Behavioural discount functions from behavioural microeconomics are embedded into a game-theoretic analysis of temptation versus enforcement to construct an encompassing model, nesting combinations of time consistent and time inconsistent preferences. The analysis presented in this paper shows that, with hyperbolic/quasihyperbolic discounting, the enforceable range of inflation targets is narrowed. This suggests limits to the effectiveness of monetary targets, under certain conditions. The paper concludes with a discussion of monetary policy implications, explored specifically in the light of current macroeconomic policy debates.

How should a group of agents decide among actions whose consequences are uncertain? I study this problem when agents and groups are subjective expected utility maximizers. A natural way to determine the preferences of a group then is relative utilitarianism with belief averaging: add up the agents' (0,1) -normalized utility functions and average their beliefs. I show that it is the only way to aggregate preferences that is monotonic in the agents' preferences and ignores preferences over redundant actions. The monotonicity condition ensures that an agent who joins a group gets to break ties in her favor if differences in preferences are due solely to differences in the utility functions.

The simple pairwise comparison is a method to provide different criteria with weights. We show that the values of those weights (in particular the maximum) depend just on the number of criteria. Additionally, it is shown that the distance between the weights is always the same. ----- Der einfache paarweise Vergleich ist ein Verfahren verschiedene Kriterien mit einer Gewichtung zu versehen. Wir zeigen, dass die Werte dieser Gewichte (insbesondere auch der maximale Wert) ausschließlich von der Anzahl der Kriterien abhängt. Darüber hinaus wird gezeigt, dass der Abstand der Gewichtungen stets gleich ist.

We show that the playing sequence--the order in which players update their actions--is a crucial determinant of whether the best-response dynamic converges to a Nash equilibrium. Specifically, we analyze the probability that the best-response dynamic converges to a pure Nash equilibrium in random n -player m -action games under three distinct playing sequences: clockwork sequences (players take turns according to a fixed cyclic order), random sequences, and simultaneous updating by all players. We analytically characterize the convergence properties of the clockwork sequence best-response dynamic. Our key asymptotic result is that this dynamic almost never converges to a pure Nash equilibrium when n and m are large. By contrast, the random sequence best-response dynamic converges almost always to a pure Nash equilibrium when one exists and n and m are large. The clockwork best-response dynamic deserves particular attention: we show through simulation that, compared to random or simultaneous updating, its convergence properties are closest to those exhibited by three popular learning rules that have been calibrated to human game-playing in experiments (reinforcement learning, fictitious play, and replicator dynamics).

We investigate how distorted, yet structured, beliefs can persist in strategic situations. Specifically, we study two-player games in which each player is endowed with a biased-belief function that represents the discrepancy between a player's beliefs about the opponent's strategy and the actual strategy. Our equilibrium condition requires that (i) each player choose a best-response strategy to his distorted belief about the opponent's strategy, and (ii) the distortion functions form best responses to one another. We obtain sharp predictions and novel insights into the set of stable outcomes and their supporting stable biases in various classes of games.