Stuart McDonald

Time-Consistent Fair Water Sharing Agreements

Scarcity of water has become a major issue facing many nations around the world. To improve the efficiency of water usage there has been considerable interest in recent years in trading water. A major issue in trading water rights is the problem of how an allocation system can be designed in perpetuity that also has desirable properties at each point of time. This is an issue of the time consistency of the contract to trade water. In this chapter we develop a model of dynamic recontracting of water rights and study time consistency properties of the resultant contracts using the ideas of Filar and Petrosjan [7].

Green Technology and Optimal Emissions Taxation

We examine the impact of an optimal emissions tax on research and development of emission reducing green technology (E-R&D) in the presence of R&D spillovers. We show that the size and effectiveness of the optimal emissions tax depends on the type of the R&D spillover: input or output spillover. In the case of R&D input spillovers (where only knowledge spillovers are accounted for), the optimal emissions tax required to stimulate R&D is always higher than when there is an R&D output spillover (where abatement and knowledge spillovers exist simultaneously). We also find that optimal emissions taxation and cooperative R&D complement each other when R&D spillovers are small, leading to lower emissions.

Income inequality and economic growth with altruistic bequests and human capital investment

In this paper we explore how income inequality affects growth in a dynastic family model with bequests (physical capital) and investment in human capital for children. For tractability, we abstract from factor markets and focus on household production, which is prevalent in developing countries. We explore a joint distribution of bequests and human capital and track the evolution of income distribution across generations. We show that initial inequality has a positive indirect effect on average output growth by lowering the ratio of physical to human capital, besides its standard negative direct effect. If education is mainly privately (publicly) provided, then income inequality retards (promotes) growth outside the balanced growth path. On the balanced growth path, inequality always hinders growth.

Using simulated annealing to calculate the trembles of trembling hand perfection

Within the literature on noncooperative game theory, there have been a number of algorithms which will compute Nash equilibria. We show that the family of algorithms known as Markov chain Monte Carlo (MCMC) can be used to calculate Nash equilibria. MCMC is a type of Monte Carlo simulation that relies on Markov chains to ensure its regularity conditions. MCMC has been widely used throughout the statistics and optimization literature, where variants of this algorithm are known as simulated annealing. We show that there is interesting connection between the trembles that underlie the functioning of this algorithm and the type of Nash refinement known as trembling hand perfection. We show that it is possible to use simulated annealing to compute this refinement.

EMISSION TAXES, CLEAN TECHNOLOGY COOPERATION, AND PRODUCT MARKET COLLUSION: EXPERIMENTAL EVIDENCE: EMISSION TAX, CLEAN R&D COOPERATION, AND COLLUSION

We use a laboratory experiment to study the link between cooperative research and development (R&D) in clean technology and collusion in a downstream product market in the presence of a time‐consistent emissions tax. Such a tax creates additional interconnections between firms, in addition to the standard technological spillovers. Our results show a strong link between R&D cooperation and market collusion under symmetric R&D spillovers in a duopoly, but when the spillovers are asymmetric, R&D cooperation does not necessarily result in collusion. With symmetric spillovers, the link between R&D cooperation and collusion remains strong even in three‐ and four‐firm industries. (JEL C90, L5, O30, Q55)

Finding traitors in secure networks using Byzantine agreements

Secure networks rely upon players to maintain security and reliability. However not every player can be assumed to have total loyalty and one must use methods to uncover traitors in such networks. We use the original concept of the Byzantine Generals Problem by Lamport [8], and the more formal Byzantine Agreement describe by Linial [10], to find traitors in secure networks. By applying general fault-tolerance methods to develop a more formal design of secure networks we are able to uncover traitors amongst a group of players. We also propose methods to integrate this system with insecure channels. This new resiliency can be applied to broadcast and peer-to-peer secure com- munication systems where agents may be traitors or be- come unreliable due to faults.

Herd behaviour as a source of volatility in agent expectations

Herd Behaviour is often cited as one of the forces behind excess volatility of stock prices as well as speculative bubbles and crashes in financial markets. This paper examines if social interaction and herd behaviour, modelled within a multi-agent framework, can explain these characteristics. The core of the model is based on the social learning literature which takes place in a small world network. We find that when the network consists entirely of herd agents then expectations become locked in an information cascade. Herd agents receive a signal, compare it with those agents with whom they are connected, and then adopt the majority position. Adding one expert agent enables the population to break the cascade as information filters from that agent to all other agents through contagion. We also find that moving from an ordered to a small world network dramatically increases the level of volatility in agent expectations and it quickly reaches a higher level (at which point increasing the randomness of the network has little effect). Increasing the influence of the experts, by increasing the number of connections from these agents, also increases volatility in the aggregate level of expectations. Finally it is found that under certain network structures herd behaviour will lead to information cascades and potentially to the formation of speculative bubbles.