Nested identification of subjective probabilities

The theory of games against nature relies on complete preferences among all conceivable acts, i.e. among all potential assignments of consequeces to states of nature (case 1). Yet most decision problems call for choosing an element from a limited set of acts. And in games of strategy, the set of strategies available to a player is givent and not amenable to artificial extensions. In “Assessing Strategic Risk”,(ECON DP 2005-20) R.J. Aumann and J.H. Drèze extend the basic result of decision theory (maximisation of subjectvely expected utility) to situations where preferences are defined only for a given set of acts, and for lotteries among these and sure consequences (case 2). In this paper, we provide a similar extension for two other situations : those where only the set of optimal elements from a given set of acts is known (case 3); and those where only a single optimal act is known (case 4). To these four cases correspond four nested sets of admissible subjective probabilities over the states or the opponent’s strategies, namely a singleton in case 1 and increasing sets in cases 2-4. The results for case 3 and 4 also define the extent to which subjective probabilities must be specified in order to solve a given decision problem or play a given name.

Kinky perceived demand curves and Keynes-Negishi equilibria

The label “Keynes-Negishi equiibria” is attached here to equilibria in a monetary economy with imperfectly competitive product and labor markets where business firms and labor unions hold demand perceptions with kinks - as posited in Negishi’s 1979 book Microeconomic Foundations of Keynesian Macroeconomics. Such equilibria are defined in a general equilibrium model, and shown to exist. Methodological implications are briefly discussed in a concluding section.Equilibrium, imperfect competition, perceived demands, kinky demand, princing rules, union wage model, union objectives, cash-in-advance

Assessing Strategic Risk

In recent decades, the concept of subjective probability has been increasingly applied to an adversary’s choices in strategic games. A careful examination reveals that the standard construction of subjective probabilities does not apply in this context. We show how the difficulty may be overcome by means of a different construction, and provide an axiomatic fondation for it.

When All is Said and Done, How Should You Play and What Should You Expect ?

Modern game theory was born in 1928, when John von Neumann published his Minimax Theorem. This theorem ascribes to all two-person zero-sum games a value - what rational players may expect - and optimal strategies - how they should play to achieve that expectation. Seventy-seven years later, strategic game theory has not gotten beyond that initial point, insofar as the basic questions of value and optimal strategies are concerned. Equilibrium theories do not tell players how to play and what to expect; even when there is a unique Nash equilibrium, it is not at all clear that the players “should” play this equilibrium, nor that they should expect its payoff. Here, we return to square one : abandon all ideas of equilibrium and simply ask, how should rational players play, and what should they expect. We provide answers to both questions, for all n-persons games in strategic form.

Imperfect competition à la Negishi also with fixed costs

The paper studies equilibria for economies with imperfect competition and non-convex technologies. Following Negishi firms maximise profits under downward-sloping perceived demand functions. Negishi's assumptions, in particular the assumption of a single monopolistic competitor in each market, are relaxed. Existence of equilibria is obtained, under otherwise standard assumptions, for production sets defined in each firm by the union of a convex technology and a technology subjected to fixed costs. In the light of a counterexample it is assumed that fixed factors are distinct from variable factors. Technically the proof rests on pricing rules.imperfect competition, fixed costs, general equilibrium, perceived demands, pricing rules

Vountary matching grants can forestall social dumping

The European economic integration leads to increasing mobility of factors, thereby threatening the stability of social transfer programs. This paper investigates the possibility to achieve by means of voluntary matching grants both the optimal allocation of factors and the optimal level of redistribution in the presence of factor mobility. We use a fiscal competition model a la Wildasin (1991) in which states differ in their technologies and preferences for redistribution. We first investigate a simple process in which the regulatory authority progressively raises the matchning grants sto the district choosing the lowest transfer and all districts respond optimally to the resulting change in transfers all around. This process is shown to increase total production and the level of redistribution. However, it does not guarantee that all districts gain, nor that an efficient level of redistribution is attained. Assuming complete information among districts, we first derive the willingness of each district to match the contribution of other districts and we show that the aggregate willingness to pay for matching rates converges to zero when both the efficient level of redistribution and the efficient outcome and guarantee that everyone will gain.Fiscal federalism, Adjustment process, Matching grants

Stock prices, anticipations and investment in general equilibrium

We propose an objective for the firm in a model of production economies extending over time under uncertainty and with incomplete markets. We derive the objective of the firm from the assumption of initial-shareholders efficiency. Each shareholder is assumed to communicate to the firm her marginal valuation of profits at all future events (expressed in terms of initial resources). In defining her own marginal valuation of the firm's profits, a shareholder takes into consideration the direct impact of a change in the value of dividends but also the impact of future dividends on the firm's stock price when she trades shares. To predict the impact on the stock price, she uses a state price process, her price theory. The firm computes its own shadow prices for profits at all date-events by simply adding up the marginal valuations of all its initial shareholders. If no restrictions are placed on individual price theories, the existence of equilibria may require financial constraints on a firm's investment when its shareholders are more optimistic than the market about the profitability of such investment. We then impose that price theories be compatible with the observed equilibrium: they should satisfy a no-arbitrage condition. We show by means of an example that, with incomplete markets and no-short selling constraints, this restriction on price theories is not enough to bring consistency in the individuals' marginal evaluations: a financial constraint on the firm's investment may still be needed to obtain an equilibriumgeneral equilibrium, incomplete markets, stock prices, anticipations, investment constraints, arbitrage

Shareholder-efficient production plans in a multi-period economy

We propose an objective for the firm in a general model of production economies extending over time under uncertainty and with incomplete markets. Trading in commodities and shares of stock occurssequentially on spot markets at all date-events. We derive the objective of the firm from the assumption of initial-shareholders efficiency.Each shareholder is assumed to communicate to the firm her marginal valuation of profits at all date events (expressed in terms of initial resources).In defining her own marginal valuation of the firm’s profits, a shareholder will take two elements into consideration. To evaluatethe direct impact of a change in dividends the shareholder uses her own vector of marginal rates of substitution for revenue across dateevents.In addition, the shareholder will take into account the impact of future dividends on the firm’s stock price when she trades shares. Topredict the effect on the stock price, she uses a (possibly different) state price process, her price theory. The only restriction that we imposeon consumers’ price theories is that they should be compatible with the observed equilibrium: given the equilibrium prices and productionplans, a price theory must satisfy a no-arbitrage condition. The firm computes its own shadow prices for profits at all date-events by simplyadding up the marginal valuations of all its initial shareholders. We prove existence of an equilibrium.