Cores of effectivity functions and implementation theory

In a committee where cooperative voting occurs, effectivity functions describe the blocking power of coalitions. It is a binary relation that says for each coalition T and each subset of outcomes B whether or not T can force the final outcome within B. The corresponding cooperative stability notion generalizes the familiar core of a simple game. We study those effectivity functions yielding a non-empty core for all preference profiles, of which additive effectivity functions are an example. This proves to be closely related to implementation by means of the strong equilibrium concept.     

Dynamic gap transformations: Are banks asset – transformers or brokers? or both?

We study the sensitivity of bank stock returns to interest rates, by extending existing tests in two important directions. We incorporate dynamic gap adjustments and extend the traditional duration gap measure to new gap measures based on the general equilibrium term structure model developed by Longstaff and Schwartz [Longstaff, F. A., & Schwartz, E. S. (1992). Interest-rate volatility and the term structure: A two-factor general equilibrium model. Journal of Finance, 47(4), 1259–1282]. Consistent with previous studies, the results indicate that banks hedge against changes in interest rate levels, when the levels are low, and speculate when the levels are high, but the volatility is low.     

Spatial pillage game

A pillage game is a coalitional game as a model of Hobbesian anarchy. The spatial pillage game introduces a spatial feature into the pillage game. Players are located in regions and can travel from one region to another. The players can form a coalition and combine their power only within their destination regions, which limits the exertion of the power of each coalition. Under this spatial restriction, a coalition can pillage less powerful coalitions without any cost. The feasibility of pillages between coalitions determines the dominance relation that defines stable states in which powers among the players are endogenously balanced. With the spatial restriction, the set of stable states changes. However, if the players have forecasting ability, then the set of stable states does not change with the spatial restriction. Core, stable set, and farsighted core are adopted as alternative solution concepts.     

Implementability via protective equilibria

We present a notion of non-cooperative strategic equilibrium for games generated by social choice functions, and fully characterize the class of those functions which are directly implementable under this equilibrium concept. Correct preference revelation turns out to always be such an equilibrium for the games generated by this class of implementable functions.     

Stable and efficient coalitional networks

We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, where the network specifies the nature of the relationship each individual has with her coalition members and with individuals outside her coalition. To predict the coalitional networks that are going to emerge at equilibrium we propose the concepts of strong stability and of contractual stability. Contractual stability imposes that any change made to the coalitional network needs the consent of both the deviating players and their original coalition partners. Requiring the consent of coalition members under the simple majority or unanimity decision rule may help to reconcile stability and efficiency. Moreover, this new framework can provide insights that one cannot obtain if coalition formation and network formation are tackled separately and independently.     

Rumours and markets

The paper presents a simple model to study the effects of rumours on markets. Agents in our economy communicate with their local neighbours which gives rise to the possible spread of a rumour. As the rumour affects beliefs of the agents the evolution of the rumour has a direct impact on market outcomes. Our results show that if the rumour dies out long-run equilibrium prices correspond to pre-rumour values. However, if the rumour stays present it produces a price run-up for the good that is positively targeted by the rumour. Price run-ups related to rumours have been observed in empirical studies by Rose [Rose, A.M., 1951. Rumor in the stock market. Public Opinion Quarterly 15, 461–486], Pound and Zeckhauser [Pound, J., Zeckhauser, R., 1990. Clearly heard on the street: the effect of takeover rumors on stock prices. Journal of Business 63, 291–308] and Zivney et al. [Zivney, T., Bertin, W.J., Torabzadeh, K.M., 1996. Overreaction to take-over speculation. Quarterly Review of Economics and Finance 36, 89–115]. The present model provides an analytical foundation for this finding.     

Limiting Dictatorial rules

We consider the preference aggregation problem in infinite societies. In our model, there are arbitrarily many agents and alternatives, and admissible coalitions may be restricted to lie in an algebra. In this framework (which includes the standard one), we characterize, in terms of Strict Neutrality, the Ultrafilter Property of preference aggregation rules. Based on this property, we define the concept of Limiting Dictatorial rules, which are characterized by the existence of arbitrarily small decisive coalitions. We show that, in infinite societies which can be well approximated by finite ones, any Arrovian rule is limiting.     

Theorems on the core of an economy with infinitely many commodities and consumers

It is known that the classical theorems of Grodal [Grodal, B., 1972. A second remark on the core of an atomless economy. Econometrica 40, 581–583] and Schmeidler [Schmeidler, D., 1972. A remark on the core of an atomless economy. Econometrica 40, 579–580] on the veto power of small coalitions in finite dimensional, atomless economies can be extended (with some minor modifications) to include the case of countably many commodities. This paper presents a further extension of these results to include the case of uncountably many commodities. We also extend Vind’s [Vind, K., 1972. A third remark on the core of an atomless economy. Econometrica 40, 585–586] classical theorem on the veto power of big coalitions in finite dimensional, atomless economies to include the case of an arbitrary number of commodities. In another result, we show that in the coalitional economy defined by an atomless individualistic model, core–Walras equivalence holds even if the commodity space is non-separable. The above-mentioned results are also valid for a differential information economy with a finite state space. We also extend Kannai’s [Kannai, Y., 1970. Continuity properties of the core of a market. Econometrica 38, 791–815] theorem on the continuity of the core of a finite dimensional, large economy to include the case of an arbitrary number of commodities. All of our results are applications of a lemma, that we prove here, about the set of aggregate alternatives available to a coalition. Throughout the paper, the commodity space is assumed to be an ordered Banach space which has an interior point in its positive cone.     

A non-cooperative interpretation of bargaining sets

This paper provides a non-cooperative interpretation for bargaining sets concepts in economic environments. We investigate the implementability of the Aumann-Maschler and Mas-Colell bargaining sets, and provide mechanisms whose subgame perfect equilibrium outcomes realize these sets. These mechanisms, in contrast to general mechanisms suggested in the implementation literature, have a natural structure closely related to that of the rationale underlying the bargaining sets. Furthermore, the strategy sets consist mainly of allocations and coalitions (thus avoiding any reference to preference parameters) and are finite dimensional. Received: 17 February 1997 / Accepted: 2 February 1999     

The politics and economics of decentralization

This paper analyzes a simple general equilibrium model with local public goods subject to exclusion and crowding. In general, no competitive equilibrium exists for such models. However, in this paper we study a four-person example, satisfying assumptions formulated in a paper by McGuire [Group segregation and optimal jurisdictions, J. Political Econ.82, 112–132 (1974)], in which a competitive equilibrium does exist. This example demonstrates that the model is capable of generating realistic implications regarding stratification of jurisdictions, the decision to subdivide or consolidate jurisdictions, reliance on exclusionary zoning, and the use of revenue sharing.     

Strategy-proof allocation when preferences are single-plateaued

Abstract. We consider private good economies with single-plateaued preferences. A solution selects for each preference profile a non-empty set of allocations. An agent strictly prefers a set of allocations to another set of allocations if and only if he strictly prefers any allocation in the first set to any in the second set according to his single-plateaued preference relation. We characterize the class of sequential-allotment solutions by essentially single-valuedness, Pareto-indifference, and coalitional stragety-proofness. These solutions are the Pareto-indifferent extensions of the solutions studied by Barberà et al. 1997. Received: 9 May 2000 / Accepted: 1 May 2001     

Multi-agent bilateral bargaining and the Nash bargaining solution

This paper studies a bargaining model where n   players negotiate how to share a pie through (n−1)$(n-1)$ bilateral bargaining sessions. In each session, two players bargain for a partial agreement that specifies who exits and who moves on to the next session (if there is any) via the alternating-proposal framework of Rubinstein [Rubinstein, A., 1982. Perfect equilibrium in a bargaining model. Econometrica 50, 97–109]. We consider two bargaining procedures under which the subgame perfect equilibrium outcomes converge to the Nash [Nash, J., 1950. The bargaining problem. Econometrica 18, 155–162] bargaining solution for the corresponding bargaining problem as the players’ discount factor goes to one. Hence, the model studied here provides a non-cooperative foundation for the Nash cooperative bargaining solution in the multilateral case.     

The Blocking Lemma for a many-to-one matching model

The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms’ preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles.     

Robust games: theory and application to a Cournot duopoly model

In this paper, the robust game model proposed by Aghassi and Bertsimas (Math Program Ser B 107:231–273, 2006) for matrix games is extended to games with a broader class of payoff functions. This is a distribution-free model of incomplete information for finite games where players adopt a robust-optimization approach to contend with payoff uncertainty. They are called robust players and seek the maximum guaranteed payoff given the strategy of the others. Consistently with this decision criterion, a set of strategies is an equilibrium, robust-optimization equilibrium, if each player’s strategy is a best response to the other player’s strategies, under the worst-case scenarios. The aim of the paper is twofold. In the first part, we provide robust-optimization equilibrium’s existence result for a quite general class of games and we prove that it exists a suitable value \(\epsilon \) such that robust-optimization equilibria are a subset of \(\epsilon \)-Nash equilibria of the nominal version, i.e., without uncertainty, of the robust game. This provides a theoretical motivation for the robust approach, as it provides new insight and a rational agent motivation for \(\epsilon \)-Nash equilibrium. In the last part, we propose an application of the theory to a classical Cournot duopoly model which shows significant differences between the robust game and its nominal version.     

Differentiated goods in a dynamic Cournot duopoly with emission charges on output

We extend the dynamic Cournot duopoly framework with emission charges on output by Mamada and Perrings (Econ Anal Policy 66:370–380, 2020), which encompassed homogeneous products in its original formulation, to the more general case of differentiated goods, in order to highlight the richness in its static and dynamic outcomes. Each firm is taxed proportionally to its own emission only and charge functions are quadratic. Moreover, due to an adjustment capacity constraint, firms partially modify their output level toward the best response. Like in Mamada and Perrings (Econ Anal Policy 66:370–380, 2020), the only steady state coincides with the Nash equilibrium, and it will be considered admissible when it guarantees the positivity of the marginal emission charge. We find that the full efficacy of the environmental policy, which applies to an equilibrium that is globally asymptotically stable anytime it is admissible, is achieved in the case of independent goods, as well as with a low good interdependence degree in absolute value, independently of being substitutes or complements. When goods are substitutes and their interdependence degree is high, the considered environmental policy is still able to reduce pollution at the equilibrium, but the latter is stable just when the policy intensity degree is large enough. When instead goods are complements and their interdependence degree is high in absolute value, the considered environmental policy produces detrimental effects on the pollution level and the unique equilibrium is always unstable, when admissible. This highlights that, from the static viewpoint, even in the absence of free riding possibilities, the choice of the mechanism to implement has to be carefully pondered, according to the features of the considered economy.

     

Virtual Nash implementation with admissible support

A social choice correspondence (SCC) is virtually implementable if it is ?$?$-close (in the probability simplex) to some (exactly) implementable correspondence [Abreu, D., Sen, A., 1991. Virtual Implementation in Nash Equilibrium. Econometrica 59, 997–1021] proved that, without restriction on the set of alternatives receiving strictly positive probability at equilibrium, every SCC is virtually implementable in Nash Equilibrium. We study virtual implementation when the supports of equilibrium lotteries are restricted. We provide a necessary and sufficient condition, imposing joint restrictions on SCCs and admissible supports. Next, we discuss how to construct supports, and we underline an important difficulty. Finally, we study virtual implementation when the support is restricted to the efficient or individually rational alternatives.     

The “probability of a fit choice”

This paper attempts to model elections by incorporating voter judgments about candidate and leader competence. The proposed model can be linked to Madison’s understanding of the nature of the choice of Chief Magistrate (Madison, James Madison: writings. The Library of America, New York, 1999 [1787]) and Condorcet’s work on the so-called “Jury Theorem” (Condorcet 1994 [1785]). Electoral models use the notion of a Nash Equilibrium. This notion generally depends on a fixed point argument. For deterministic electoral models, there will typically be no equilibrium. Instead we introduce the idea of a preference field, $H,$ for the society. A condition called half-openess of $H$ is sufficient to guarantee existence of a local direction gradient, $d,$ Even when $d$ is not well-defined we can use the idea of the heart for the society. This is an attractor of the set of social moves that can occur. As an application, a stochastic model of elections is considered, and applied to the 2008 presidential election in the United States. In such a stochastic model the electoral origin will satisfy the first order condition for a local Nash equilibrium. We then show how to compute the Hessian of each candidate’s vote share function, and obtain necessary and sufficient conditions for convergence to the electoral origin, suggesting that there will be a social direction gradient. The origin maximizes aggregrate voter utility and can be interpreted as a fit choice for the polity.     

Investing equally in risk

Classical optimal strategies are notorious for producing remarkably volatile portfolio weights over time when applied with parameters estimated from data. This is predominantly explained by the difficulty to estimate expected returns accurately. In Lindberg (Bernoulli 15:464–474, 2009), a new parameterization of the drift rates was proposed with the aim to circumventing this difficulty, and a continuous time mean–variance optimal portfolio problem was solved. This approach was further developed in Alp and Korn (Decis Econ Finance 34:21–40, 2011a) to a jump-diffusion setting. In the present paper, we solve a different portfolio problem under the market parameterization in Lindberg (Bernoulli 15:464–474, 2009). Here, the admissible investment strategies are given as the amounts of money to be held in each stock and are allowed to be adapted stochastic processes. In the references above, the admissible strategies are the deterministic and bounded fractions of the total wealth. The optimal strategy we derive is not the same as in Lindberg (Bernoulli 15:464–474, 2009), but it can still be viewed as investing equally in each of the n Brownian motions in the model. As a consequence of the problem assumptions, the optimal final wealth can become non-negative. The present portfolio problem is solved also in Alp and Korn (Submitted, 2011b), using the L ²-projection approach of Schweizer (Ann Probab 22:1536–1575, 1995). However, our method of proof is direct and much easier accessible.     

Myopia and pensions in general equilibrium

The US social security tax rate has doubled in the last half century. Does the degree of myopic behavior that we observe in the US justify the size of the social security program? To study this question we build a computable general equilibrium model that is composed of life-cycle permanent-income consumers who save optimally and “hand-to-mouth” consumers who just consume their disposable income. Our model is a continuous-time, general equilibrium extension of the model by Cremer et al. (Int Tax Public Financ 15(5):547–562, 2008), though we abstract from the redistributive function of social security to focus on myopia. Retirement is a choice variable in our model and the social security program is designed to mimic the US program in which the annuity value of benefits increases with the retirement age. Also, we allow for delayed claiming beyond the date of retirement. The model matches a variety of important data targets relating to saving and retirement. We find that small reductions in the social security tax rate provide significant welfare gains to both groups of consumers.     

Generic non-existence of general equilibrium with EUU preferences under extreme ambiguity

In the presence of three or more realisations of the aggregate endowment that are extremely ambiguous, in the sense that all relative probabilities are admissible, if agents have preferences that are representable by expected uncertain utility functions (Gul and Pesendorfer, 2014), general equilibrium does not generically exist in finite economies. It always exists, however, in continuum economies.