Abstract
Both corruption and market imperfections are important facets of modern arms markets. In the standard literature of arms market, production, procurement, sales (exports) and purchases (imports) of arms take place in the shadow of corruption. Corruption is an integral part of the environment of the arms trade that exerts an influence upon the outcome in the arms market. In our work, we make corruption as a choice variable of the powerful players in the global arms market and examine the equilibrium consequence of corruption that is strategically chosen by armament firms. We develop a simple duopoly to characterize a perfect Nash equilibrium of cash-for-favors and establish perplexing comparative static properties of this equilibrium. The primary intuition here is that cash-for-favors can have serious impacts on the equilibrium of an oligopoly through their effects on the incentives of and constraints on individual firms. We offer a model of endogenous corruption, to our understanding for the first time, to examine the global arms market in order to establish that the equilibrium outcome in the arms market cannot be fully captured by the standard results of oligopoly. Researchers have to extremely careful in applying the standard tools of oligopoly to the arms market as our results suggest that endogenous corruption can reverse most of the known results of oligopoly.
Appendix
Proof of observation 1
The profit function of each firm at Stage II of the game is given by the following equations derived in the text:
From the first derivative of (2a) and (2a′) we get the first order condition as the following equations:
The second order condition holds as the second derivative of the profit function with respect to Xi is –2b and since b>0 from the downward sloped demand function. The reaction functions of the firms are given as the following:
The Cournot-Nash equilibrium is given by the values of X1 and X2 that simultaneously satisfy (A.1.1) and (A.1.2). Solving (A.1.1) and (A.1.2) simultaneously, we get the Cournot-Nash outputs as:
If
Substituting (A.1.3) and (A.1.4) in the demand function will give the price. QED.
Proof of proposition 1
In the text we have derived the profit function from the arms industry as the following:
Differentiating the first term of the right hand side (RHS) of (3f) with respect to T yields:
Let us call the second term of the RHS of (3f) H:
Substituting the Cournot-Nash equilibrium values of
The equilibrium in the overall game calls forth the following first order condition:
The second order condition requires
Substituting (B.1.1) and (B.1.4) yields the optimal T* as:
Substituting (B.1.2) and (B.1.5) into (B.1.7) yields the second order condition for the maximization overall profits from the two-stage game as:
Simplification of (B.1.8) yields the second order condition for the overall maximization of profits from the two-stage game:
QED.
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