Department of Economics
University of Birmingham
Edgbaston B15 2TT, UK
[o] Room 220, J. G. Smith building
[t] +44 121 414 3754
[f] +44 121 414 7377
[e] c.rowat@bham.ac.uk
Office hours: 1:00 - 2:00pm Mon, 11:00 - 12:00 Tue
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Non-linear strategies in a linear quadratic
differential game.
Journal of Economic Dynamics and Control, vol 31(10), pp. 3179 - 3202, October 2007.
The commons with capital markets, with J. Dutta.
Economic Theory, vol 31(2), pp. 225-254, May 2007.
Intermediation by aid agencies, with P.
Seabright.
Journal of Development Economics, vol 79(2), pp. 469 - 491, April 2006.
Stable Sets in Three Agent Pillage Games , with M. Kerber.
June 2009, Department of Economics Discussion Paper, University of Birmingham, 09-07.
Jordan (2006, JET) characterises stable sets for three special cases of ‘pillage games’. For anonymous, three agent pillage games we show that: when the core is non-empty, it must take one of five forms; all such pillage games with an empty core represent the same dominance relation; when a stable set exists, and the game also satisfies a continuity and a responsiveness assumption, it is unique and contains no more than 15 elements. This result uses a three step procedure: first, if a single agent can defend all of the resources against the other two, these allocations belong to the stable set; dominance is then transitive on the loci of allocations on which the most powerful agent can, with any ally, dominate the third, adding the maximal elements of this set to the stable set; finally, if any allocations remain undominated or not included, the game over the remaining allocations is equivalent to the ‘majority pillage game’, which has a unique stable set [Jordan and Obadia, 2004, “Stable sets in majority pillage games”, mimeo]. Non-existence always reflects conditions on the loci of allocations along which the most powerful agent needs an ally. The analysis unifies the results in Jordan when n = 3.
A Ramsey bound on Jordan stable sets, with M. Kerber.
March 2009, Department of Economics Discussion Paper, University of Birmingham, 09-01R.
Jordan (2006, JET) defined `pillage games', a class of cooperative games whose dominance operator represents a `power function' constrained by monotonicity axioms. In this environment, he proved that stable sets must be finite. We bound their cardinality above by a Ramsey number and show this bound to be tight for two agents. More generally, it is not tight as it does not make use of structural information across partial orders on the stable set.
The accompanying LISP code is available here.
The road to extinction: commons with
capital markets, with J. Dutta.
January 2007, Department of Economics Discussion Paper, University of Birmingham, 04-11RR.
We study extinction in a commons problem in which agents have access to
capital markets. When the commons grows more quickly than the interest
rate, multiple equilibria are found for intermediate commons
endowments. In one of these, welfare decreases as the resource becomes
more abundant, a `resource curse'. As marginal extraction costs
become constant, market access instantly depletes the commons. Without
markets - the classic environment - equilibria are unique; extinction
dates and welfare increase with the endowment. When the endowment is
either very abundant or very scarce, market access improves welfare. As
marginal costs of extraction from the commons become constant, market
access can reduce welfare if the subjective discount rate exceeds the
interest rate.
Revises Discussion Paper 04-11 (May 2004)
Optimal two stage committee voting rules, with I. Ayres and N. Zakariya.
March 2007, Department of Economics Discussion Paper, University of Birmingham, 04-23RR.
We study option management by committee. Analysis is illustrated by tenure
decisions. Our innovations are two-fold: we treat the committee's problem as
one of social choice, not information aggregation; and we endogenise the
outside option: rejecting a candidate at either the probationary or tenure
stage return the committee to a candidate pool. For committees with N members,
we find: (1) a candidate's fate depends only on the behaviour of two
`weather-vane' committee members - generalised median voters; (2) enthusiastic
assessments by one of these weather-vanes may harm a candidate's chances by
increasing others' thresholds for hiring him; and (3) sunk time costs may lead
voters who opposed hiring a candidate to favour tenuring him, even after a poor
probationary performance. We characterise the optimal voting rule when N=2. A
patient or perceptive committee does best with a (weak) majority at the hiring
stage and unanimity at the tenure stage. An impatient or imperceptive
committee does best under a double (weak) majority rule. If particularly
impatient or imperceptive, this rule implies that any hire is automatically
tenured. Perversely, the performance of a patient, imperceptive committee
improves as its perceptiveness further declines.
Revises Discussion Paper 04-23 (November 2004).
Functional Nash equilibria in commons games
August 2002, Department of Economics Discussion Paper, University of Birmingham, 02-13.
This paper explores functional Nash equilibria in three static commons problems. The first
yields a non-existence result. Two linear equilibrium strategies are found in the second.
Unlike the result in Klemperer and Meyer (1989, Eca), this is unaffected by the domain of the stochastic variable. The third model finds two FNE when the second's strategy space is expanded to allow transfers. While these equilibria are improvements over their equivalents in the second model, the models cannot be Pareto ranked.
Asymmetric play in a linear quadratic differential game with bounded controls
August 2002, Department of Economics Discussion Paper, University of Birmingham, 02-12.
This paper uses computational techniques to identify the Markov perfect equilibria in a two agent linear quadratic differential game with bounded controls. No evidence is found of asymmetric equilibria when the agents are symmetric or of non-linear equilibria when the agents are asymmetric. This suggests that the standard continuum result for identical agents is not robust and that non-linear strategies are not of general interest in the analysis of linear quadratic differential games. The techniques presented here are applicable to a broader class of differential games as well.
Additive Externality Games, November 2000, PhD thesis, University of Cambridge (revised November 2001). This thesis attempts to address the question of how national greenhouse gas emissions might be set in the absence of an international enforceable treaty. It explores differential game models to first ask how emissions might be set when nations interact exclusively through their emissions. It then explores a one-shot game in which nations set transfer functions as well as emissions functions.
v2a.c is the C code used to assess asymmetric play in the linear quadratic differential games examined above. vf.data is a sample data file.
"Technological and regulatory developments in broadcasting: an overview", in The Economic Regulation of Broadcasting Markets (eds. Paul Seabright and Jürgen von Hagen), Cambridge University Press, 2007.
ESRC grant RES-156-25-0022: Weak Property Rights: Financial Markets and Development (World Economy and Finance Programme), with J Dutta, April 2005 - March 2009.
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