Optimism and commitment: An elementary theory of bargaining and war

We propose an elementary theory of wars fought by fully rational contenders. Two parties play a Markov game that combines stages of bargaining with stages where one side has the ability to impose surrender on the other. Under uncertainty and incomplete information, in the unique equilibrium of the game, long confrontations occur: war arises when reality disappoints initial (rational) optimism, and it persist longer when both agents are optimists but reality proves both wrong. Bargaining proposals that are rejected initially might eventually be accepted after several periods of confrontation. We provide an explicit computation of the equilibrium, evaluating the probability of war, and its expected losses as a function of i) the costs of confrontation, ii) the asymmetry of the split imposed under surrender, and iii) the strengths of contenders at attack and defense. Changes in these parameters display non-monotonic effects.

Testing the Tunnel Effect: Comparison, Age and Happiness in UK and German Panels

In contrast to previous results combining all ages we find positive effects of comparison income on happiness for the under 45s, and negative effects for those over 45. In the BHPS these coefficients are several times the magnitude of own income effects. In GSOEP they cancel to give no effect of effect of comparison income on life satisfaction in the whole sample, when controlling for fixed effects, and time-in-panel, and with flexible, age-group dummies. The residual age-happiness relationship is hump-shaped in all three countries. Results are consistent with a simple life cycle model of relative income under uncertainty.