Necessary and sufficient conditions for a resolution of the social choice paradox

We present a restriction on the domain of individual preferences that is both necessary and sufficient for the existence of a social choice rule that is continuous, anonymous, and respects unanimity. The restriction is that the space of preferences be contractible. Contractibility admits a straightforward intuitive explanation, and is a generalisation of conditions such as single peakedness, value restrictedness and limited agreement, which were earlier shown to be sufficient for majority voting to be an acceptable rule. The only restriction on the number of individuals, is that it be finite and at least 2.social choice; preferences; mathematical modeling

You Only Die Once: Managing Discrete Interdependent Risks

This paper extends our earlier analysis of interdependent security issues to a general class of problems involving discrete interdependent risks with heterogeneous agents. There is a threat of an event that can only happen once, and the risk depends on actions taken by others. Any agent's incentive to invest in managing the risk depends on the actions of others. Security problems at airlines and in computer networks come into this category, as do problems of risk management in organizations facing the possibility of bankruptcy, and individuals' choices about whether to be vaccinated against an infectious disease. Surprisingly the framework also covers certain aspects of investment in R&D. Here we characterize Nash equilibria with heterogeneous agents and give conditions for tipping and cascading of equilibria.

Managing unknown risks: the future of global reinsurance

It has been said that insurance is the last of the financial services to accept radical change (Denney [1995-1996]). Yet there has been a fundamental shift in the geographic location and in the organization of the reinsurance industry in the last six years (Chichilnisky [19966]). Global environmental risks are partly responsible for this change; increased weather volatility and catastrophic risks are difficult to diversify using traditional insurance practices. To provide a map to the future, we need a realistic appraisal of how we got where we are. This is the story of how humans have hedged risks. There are two basic and distinct approaches: statistical and economic. The former is typical of the insurance industry; the latter typifies the securities industry. Both are needed to manage today's catastrophic risks. Neither alone will do. We show how a combination of both leads to efficient outcomes, and is the way to the future (Chichilnisky [1996a, 1996b, 1996d]).insurance; risk; global finance; environment; catastrophe bundles; climate change

Interdependent Security: The Case of Identical Agents

Do firms have adequate incentives to invest in anti-terrorism mechanisms? This paper develops a framework for addressing this issue when the security choices by one agent affect the risks faced by others. We utilize the airline security problem to illustrate how the incentive by one airline to invest in baggage checking is affected by the decisions made by others. Specifically if an airline believes that others will not invest in security systems it has much less economic incentive to do so on its own. Private sector mechanisms such as insurance and liability will not necessarily lead to an efficient outcome. To induce adoption of security measures one must turn to regulation, taxation or institutional coordinating mechanisms such as industry associations. We compare the airline security example with problems having a similar structure (i.e., computer security and fire protection) as well as those with different structures (i.e., theft protection and vaccinations). The paper concludes with suggestions for future research.

Social Reinforcement: Cascades, Entrapment and Tipping

There are many social situations in which the actions of different agents reinforce each other. These include network effects and the threshold models used by sociologists (Granovetter, Watts) as well as Leibenstein's "bandwagon effects." We model such situations as a game with increasing differences, and show that tipping of equilibria as discussed by Schelling, cascading and Dixit's results on clubs with entrapment are natural consequences of this mutual reinforcement. If there are several equilibria, one of which Pareto dominates, then we show that the inefficient equilibria can be tipped to the efficient one, a result of interest in the context of coordination problems.

Energy-Capital Substitution: A General Equilibrium Analysis

We consider an economy which imports energy from a monopolistic price-setter. The domestic general equilibrium of this economy adjusts in response to the price of energy. We define the total cross price elasticity of demand between energy and capital as the cross price elasticity across general equilibria of the economy, as the equilibrium changes in response to energy price changes. This corresponds to the price elasticity given by a total demand curve, and incorporates adjustments on both supply and demand sides. It is shown that whether this total elasticity implies energy-capital complementarity or substitutability depends upon the parameters of the model and the price of energy: for a given model, there may be a change from substitutability to complementarity as the price of energy rises. This framework offers an additional way of reconciling apparently conflicting findings on energy-capital complementarity and substitutability: an earlier suggestion was made by Berndt and Wood (1979). It is a natural extension of the general equilibrium approach initiated by Hogan (1977).price elasticity; substitutability; complementarity; energy; energy prices; general equilibrium; monopoly

Supermodularity and Tipping

We model tipping as a game-theoretic phenomenon and investigate the connection between supermodular games, tipping of equilibria and cascading, and apply the results to issues that arise in the context of homeland security and computer security. We show that tipping and cascading can occur in supermodular games and that "increasing differences"is a sufficient condition for tipping. Supermodularity and tipping of equilibria are closely related. We relate our results to Schelling%u2019s early work on tipping.

Technology diffusion, abatement cost, and transboundary pollution

This paper studies countries’ incentives to develop advanced pollution abatement technology when technology may spillover across countries and pollution abatement is a global public good. We are motivated in part by the problem of global warming: a solution to this involves providing a global public good, and will surely require the development and implementation of new technologies. We show that at the Nash equilibrium of a simultaneous-move game with R&D investment and emission abatement, whether the free rider effect prevails and under-investment and excess emissions occur depends on the degree of technology spillovers and the effect of R&D on the marginal abatement costs. There are cases in which, contrary to conventional wisdom, Nash equilibrium investments in emissions reductions exceed the first-best case.International environmental agreement; pollution abatement costs; endogenous technological change.

Equivalence of saddle-points and optima for non-concave programmes

AbstractA basic result of optimisation theory is that a saddle-point of the Lagrangian is an optimum of the associated programming problem, independently of any concavity assumptions. It is also well known that under concavity assumptions the two are equivalent; i.e., an optimum is always a saddle-point. It is demonstrated that this basic equivalence of saddle-points and optima in fact holds for a much larger class of problems, which are not necessarily concave, but are equivalent to concave programmes up to a diffeomorphism. This class generalises the class of geometric programmes