Information Advantage in Cournot Oligopoly with Separable Information, or Nondifferentiable

Einy et al (2002) showed that information advantage of a firm is rewarded in any equilibrium of an incomplete information Cournot oligopoly, provided the inverse demand function is differentiable and monotonically decreasing, and costs are affine. We extend this result in two directions. We show first that a firm receives not less than its rival even if that firm's information advantage is only regarding payoff-relevant data, and not necessarily payoff-irrelevant "sunspots". We then show that there is at least one equilibrium which rewards firm's information advantage even with non-differentiable, but concave, inverse demand function. Under certain conditions, these results hold even with always non-negative inverse demand functions.Oligopoly, Incomplete Information, Information advantage, Bayesian Cournot, Equilibrium, Sunspots, Non-differentiability, Inverse demand

Payoffs in Non-Differentiable Perfectly Competitive TU Economies

We show that a single-valued solution of non-atomic finite-type market games (or perfectly competitive TU economies underlying them) is uniquely determined as the Mertens value by four plausible value-related axioms. Since the Mertens value is always in the core of an economy, this result provides an axiomatization of a core-selection (or, alternatively, a competitive payoff selection).

Unilateral Deviation with Perfect Information

For extensive form games with perfect information, consider a learning process in which, at any iteration, each player unilaterally deviates to a best response to his current conjectures of others' strategies; and then updates his conjectures in accordance with the induced play of the game. We show that, for generic payoffs, the outcome of the game becomes stationary in finite time, and is consistent with Nash equilibrium. In general, if payoffs have ties or if players observe more of each others' strategies than is revealed by plays of the game, the same result holds provided a rationality constraint is imposed on unilateral deviations: no player changes his moves in subgames that he deems unreachable, unless he stands to improve his payoff there. Moreover, with this constraint, the sequence of strategies and conjectures also becomes stationary, and yields a self- confirming equilibrium.Extensive form games with perfect information, self-confirming and Nash equilibria, unilateral deviations, objective updates, convergence in finitely many steps

Characterization of the Shapley-Shubik Power Index Without the Efficiency Axiom

We show that the Shapley-Shubik power index on the domain of simple (voting) games can be uniquely characterized without the e¢ ciency axiom. In our axiomatization, the efficiency is replaced by the following weaker require- ment that we term the gain-loss axiom: any gain in power by a player implies a loss for someone else (the axiom does not specify the extent of the loss). The rest of our axioms are standard: transfer (which is the version of additivity adapted for simple games), symmetry or equal treatment, and dummySimple Games, Shapley-Shubik Power Index, Effciency Axiom

Optimal Scrutiny in Multi-Period Promotion Tournaments

Consider a principal who hires heterogeneous agents to work for him over T periods, without prior knowledge of their respective skills, and intends to promote one of them at the end. In each period the agents choose effort levels and produce random outputs, independently of each other, and are fully informed of the past history of outputs. The principal's major objective is to maximize the total expected output, but he may also put some weight on detecting the higher-skilled agent for promotion. To this end, he randomly samples n out of the T periods and awards the promotion to the agent who produces more on the sample. This determines an extensive form game Gamma (T,n), which we analyze for its subgame perfect equilibria in behavioral strategies. We show that the principal will do best to always choose a small sample size n. More precisely, if eta(T) is the maximal optimal sample size, then eta(T)/T approaches 0 as T approaches infinity.Multi-period promotion tournaments, extensive form games, subgame perfect equilibria, undominated sample sizes

Continuity of the value and optimal strategies when common priors change

We show that the value of a zero-sum Bayesian game is a Lipschitz continuous function of the players?common prior belief, with respect to the total variation metric (that induces the topology of setwise convergence on beliefs). This is unlike the case of general Bayesian games, where lower semi-continuity of Bayesian equilibrium payo¤s rests on the convergence of conditional beliefs (Engl (1995), Kajii and Morris (1998)). We also show upper, and approximate lower, semi- continuity of the optimal strategy correspondence with respect to the total variation norm, and discuss approximate lower semi-continuity of the Bayesian equilibrium correspondence in the context of zero-sum games.Zero-Sum Bayesian Games, Common Prior, Value, Optimal Strategies, Upper Semi-Continuity, Lower Approximate Semi- Continuity.

Continuity of the value and optimal strategies when common priors change

We show that the value of a zero-sum Bayesian game is a Lipschitz continuous function of the players' common prior belief, with respect to the total variation metric (that induces the topology of setwise convergence on beliefs). This is unlike the case of general Bayesian games, where lower semi-continuity of Bayesian equilibrium payoffs rests on the convergence of conditional beliefs (Engl (1994), Kajii and Morris (1998)). We also show upper, and approximate lower, semi-continuity of the optimal strategy correspondence with respect to the total variation norm, and discuss approximate lower semi-continuity of the Bayesian equilibrium correspondence in the context of zero-sum games.Zero-Sum Bayesian Games, Common Prior, Value, Optimal Strategies, Upper Semi-Continuity, Lower Approximate Semi-Continuity

Prizes versus Wages with Envy and Pride

We show that if agents are risk neutral, prizes outperform wages when there is sufficient pride and envy relative to the noisiness of performance. If agents are risk averse, prizes are a necessary supplement to wages (as bonuses).Envy, Pride, Wages, Prizes, Bonus

Prizes versus Wages with Envy and Pride

We show that if agents are risk neutral, prizes outperform wages if and only if there is sufficient pride and envy relative to the noisiness of performance. If agents are risk averse, prizes are a necessary supplement to wages (as bonuses).Envy, Pride, Wages, Prizes, Bonus