RUPAYAN GUPTA ROGER WILLIAMS UNIVERSITY November 8, 2012 Designing Institutions for Global Security

Background Countries facing a common threat to their national security often form alliances to counter it Examples  Common action during the first Gulf War  Common action against nuclear non-proliferation  Common action by NATO states during the Cold War

Questions  How can the alliance achieve an optimal level of effort when security has public effects – both positive and negative externalities?  Role of international institutions (like the NATO) in achieving this?  Do we need to design international institutions in a particular fashion?  What role does multilateral participation have?

Literature Economics of Alliances  Olson & Zeckhauser (1966)  Weber & Wiesmeth (1991)  Sandler (1997)  Niou & Tan (2005)  Sandler & Siqueira (2006)  Gupta (2010, 2012a, 2012b)

Literature International Relations Literature Koremenos, Lipson, Snidal (2001a, 2001b) Wendt (2001) Use of Bargaining Theory & Mechanism Design in resolving conflicts Muthoo (2004) Sjostrom & Maskin (2002)

Environment Finite number of countries (governments) i=1,2,…I, form an alliance against an external threat by a “rogue nation” Endogenous level of threat: t Є [0,∞) The governments play a non-cooperative simultaneous-move game of complete information, with the rogue country also moving simultaneously

Environment Decision variables of the governments: m i Є [0,∞) : Consumption of private good e i Є [0,∞) : Security effort by i Utility from joint effort for government i: U i (.) = U of private good + U of security - Negative effect of effort = m i + S i (e,t ) - N i (e,t)

Environment Utility from joint effort of country i is: U i (.) = m i + λ i (t)e – e 2 Where, m i : Private good (money) e = ∑ i=1 I e i : Joint security effort of the bloc λ i (.) : A private variable of i, λ i Є (0,∞) – level of “public support” for security λ ’ (t)>0 (Single-peaked utility functions with different ideal points of security effort for countries)

Environment i’s Budget constraint: m i + C(e i ) ≤ M i Where, M i = initial endowment of private good Linear Costs: C(e i ) = ce i, c > 0 The payoff (net benefit) of a country from effort is: V i = M i + λ i ( t)∑ i=1 I e i – (∑ i=1 I e i ) 2 - ce i

The Rogue State Utility of the rogue state: U l (.) = m l + α l (e)t – t 2 Where, m l : Private good (money) α l (.) : A preference index of the rogue nation t: The threat effort α ' (e) <0 The rogue nation’s budget constraint: m l + vt ≤ M l

Nash equilibrium of the non-cooperative simultaneous effort choice game  In equilibrium, country I with λ I >λ i, for i ≠ I, makes all of the joint effort against a level of threat, while all other countries in the bloc make no effort. This equilibrium is unique.  The Nash outcome is given by the alliance’s effort profile: (e 1, e 2,….., e I-1, e I ) = (0, 0,….., ½[λ I (t N ) - c]) The rogue nation makes threat effort: t N =½[λ I (e N ) - v])  The effort level for the alliance in equilibrium is: e N = e I = ½[λ I (t N ) – c] We have a Unilateral outcome. Some alliance members might benefit if the unilateral effort level was reduced

Efficiency Maximizing the Benthamite SWF Max {e} ∑ i=1 I V i = ∑ i=1 I M i + e ∑ i=1 I λ i (t) – Ie – ce The efficient solution: e E = ½I[∑ i=1 I λ i (t E ) – c] The efficient level of joint effort may not be same as the unilateral level Notice that the public support index has changed, as the threat level would change in response to a changing effort level

Comparison of the efficient and unilateral outcomes Lemma: The efficient level of joint effort is lesser (greater) than the unilateral outcome if the ex ante λ I is ‘sufficiently’ higher (not higher) than the average value of ex post λ i for all countries (i.e. ∑ i=1 I λ i /I) If the security effort at the unilateral outcome is greater (lesser) than at the efficient outcome, then the threat level is lesser (greater) at those respective outcomes, and vice versa. Assumption: Ex post nation I still has highest λ

Institution Design Can an institutional structure for the alliance help to reach the efficiency point, for e E < e N ? Consider the following game: (Called the ‘Institutional game’ in the paper) There are the original I players in this game, plus a ‘neutral’ player. There are four stages in this game.

The Institutional Game  The 1 st stage: Proposal stage The neutral player makes a proposal [P, R, {T}, e i = (0, 0,….., e E )], where P is a set of payees R is a set of recipients {T} is a transfer vector describing amounts paid by payees and received by recipients e i = (0, 0,….., e E ) is a particular effort vector  The 2 nd stage: Voting stage The payees and I vote to adopt the proposal under Unanimity rule

The Institutional Game  The 3 rd stage: Effort stage If proposal is adopted, there is an effort choice game involving transfers played by the players excluded from voting in the 2 nd stage For non-adoption, there is the non-cooperative effort choice game  The 4 th stage: Payments made upon observation of effort or money given back to payees Note: All players rational and have complete information.

The Main Result  There exists:  A set of payees  A set of recipients  Amounts of payments and receipts that the neutral player can propose For which,  The players’ strategy profile ({Agree, e i = 0 for NP} {iЄP}, { e i = 0 for P & NP} {i Є R\I and Φ i 0},{ Agree, e I = e N for NP }I) is a subgame perfect equilibrium of the institutional game.

The Sub-game Perfect Outcome In the institutional game all payees & I vote to pass the neutral player's proposal in the voting round The recipients (other than I) make no effort in the effort choice round In this outcome, the joint effort of the alliance is at the efficient level, with effort being solely made by nation I

Some Implications For efficient security greater than unilateral level, the ex post level of public support should be sufficiently close to the ex ante support, for payee nations to support the scheme Note: For higher security levels, threat is lower, hence public support is lower and vice versa For efficient level lower than the unilateral level, the payee nations would typically need to have ex post levels of the public support which are sufficiently greater than the ex ante levels

Relaxing the assumption λ’(t)>0 (λ’(t)<0 for payees only) When the efficient level is higher than the unilateral level the transfer needed to shift to efficiency is more than in the earlier case However, the maximum amount the payee countries are willing to pay to move also goes up, as the escalation of the threat increases public support Note: Efficiency point even higher than before When efficient security level is less than the unilateral level, the maximum amount payee countries are willing to pay goes down, as the escalation of the threat decreases public support The transfer amount needed maybe more or less Note: Efficiency point even lower than before These factors have implications for achieving ex post efficiency constraint, hence on workability of the suggested institution