A Dynamic Model of Conflict and Cooperation

use of the stock does diminish its availability to other agents, and is open to appropriation by
rivals due to the lack of well-defined or enforceable property rights. Hence each of the agents is
tempted by the immediate benefit attainable from capturing the stock. Natural resources and
land in primitive historical societies are examples of such durable stocks or disputed wealth.

We model the incentives of agents to exert effort in an attempt to defend their claims on
the stock and challenge the claims of others. All agents who succumb to the temptation reduce
their help in production of the common-pool stock to increase their efforts to convert claims
on the common stock into effective property rights. More specifically, agents derive utility
(or a payoff) from owning the stock of durable good and, at every instant in time, choose
how to allocate an endowment between appropriation of the common-pool stock (creating
property rights) and participating in the production process to accumulate the common-pool
stock in the economy. The production and appropriation decisions made independently and
noncooperatively by each of the contenders jointly determine the evolution of the commonly
accessible stock.

We present a tractable version of a differential game formulation of this model of conflict
between several agents who attempt to appropriate a common-pool durable stock over an in-
finite horizon. The solution concept employed is Markov perfect (MP) equilibrium, restricting
strategies to be functions of the current payoff-relevant state variable. Not all the strategies
that describe a solution of the intertemporal optimizing problem of an agent are MP equi-
libria. The key to determining which describe equilibrium outcomes is subgame perfection
over the global domain of a state variable. In spite of this natural but stringent requirement,
there are multiple non-linear MP equilibrium strategies in our model. This multiplicity of
strategies has the following characteristics and implications. First, most of those solutions
commonly reveal that initially poor countries will exhibit an increase in appropriation as the
aggregate stock of durable good gets larger until a steady state is reached. Second, on the
other hand, in economies with an affluent endowment of natural resources the ‘marginal gain’
of appropriation is high and agents substitute appropriation for production for a while until
the state variable reaches a threshold level. From that threshold onwards, agents choose to
engage in production activity to some extent until a steady state is reached where the output

<<   3   4   5   6   7   8   9   >>

More intriguing information