Globalism and Regionalism: The East Asian Currency Crisis and Institutional Building

Motoshi Suzuki

doi:10.1007/978-4-431-56466-9_11

Games of Conflict and Cooperation in Asia pp 249-270 | Cite as

Globalism and Regionalism: The East Asian Currency Crisis and Institutional Building

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Motoshi Suzuki

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First Online: 08 February 2017

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Part of the The Political Economy of the Asia Pacific book series (PEAP)

Abstract

Two issues arise when building a regional institution. States must coordinate their choices on the arrangements, which is often complicated by asymmetric information where states have differing expectations about appropriate institutional arrangements. In East Asia, coordination and information problems are aggravated by regional rivalries that constrain the flow of interstate communications. This chapter analyzes these problems using game-theory models with empirical references to the East Asian currency crisis and subsequent efforts at building a regional currency management institution. Successful institutional building promotes information sharing and the convergence of states’ expectations, which facilitate coordination through either an interstate (intra-regional) communication channel or delegation to a global (extra-regional) institution. Indeed, while creating a regional agreement on foreign reserve swaps between states’ central banks or the Chiang Mai Initiative (CMI) to prevent another crisis, East Asian states used an institutional link to the International Monetary Fund (IMF) as a mechanism to overcome these problems and relied on an intra-regional communication channel, the ASEAN plus Three (APT) framework, to realize a more autonomous CMI and to reduce regional rivalries.

Keywords

Communication Asymmetric information Cheap talk Chiang-Mai Initiative (CMI) International Monetary Fund (IMF)

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Appendix 11.1 Babbling Equilibrium

If c > 0, then J and M have divergent preferences. J proposes r to maximize its utility unilaterally. M knows that J has an incentive to misrepresent its true preference and consequently disregards r. M uses its prior belief of a uniform distribution to predict w and determine f. Because M ignores r, J’s best response is to propose r at any point between 0 and 1, irrespective of w. Because M cannot confirm J’s proposal, J has no incentive to reveal its true preference. Thus, J’s proposal is not self-signaling and J offers the same proposal regardless of the true value of w. This is a pooling equilibrium or a babbling equilibrium under which no meaningful information is transmitted from J to M.

Consider the states’ utilities under a babbling equilibrium. M chooses the value of f to maximize its expected utility under the condition that there is no other meaningful information but its prior belief of a uniform distribution of w over [0, 1], which can be denoted as the density function h(w)=1 for w. M’s expected utility is given by

$$ {EU}_M^B={\int}_0^1-{\left(\,f-w\right)}^2h(w) dw. $$

Solving the equation gives

$$ {EU}_M^B=-{f}^2+f-\frac{1}{3} $$

The first-order condition is given by $ \frac{dEU_M^B}{df}=-2f+1=0. $

This yields $ f=\frac{1}{2} $

Under a babbling equilibrium, M’s expected utility can be computed from Eq. (11.1) in the main text and $ f=\frac{1}{2}\kern0.5em $as $ {EU}_M^B=-\frac{1}{12} $. By combing the above result and Eq. (11.2) in the main text, J’s expected utility is $ {EU}_J^B=-\left(\frac{1}{12}+{c}^2\right) $.

Appendix 11.2 Conditions for Partitioning

As noted in the main text, J partitions f ( f ∈[0, 1]) into two intervals at point w₁ and proposes r within each interval. J extends r₁ for the interval [0 , w₁) and r₂ for the interval [w₁, 1]. The quadratic loss function for J’s utility is symmetric at its ideal point, which is denoted by w₁ + c. For the two proposals to be in equilibrium, both need to provide J with equivalent utilities. In other words, the distance between f₁ pertaining to r₁ and J’s ideal point, w₁ + c has to be equal to the distance between f₂ pertaining to r₂ and J’s ideal point, w₁ + c. If this equidistance condition does not hold, there is no rationale for the partition (or no rationale for two proposals) and J would make a single proposal that produces a higher utility. Thus, the following condition is necessary for partitioning:

$$ {w}_1+c=\frac{1}{2}\left(\frac{w_1}{2}+\frac{w_1+1}{2}\right). $$

Rearranging this equation gives

$$ {w}_1=\frac{1}{2}-2c. $$

To make partitioning possible, w₁ > 0 and $ c<\frac{1}{4} $.

If J’s bias (c) approaches the critical value of $ \frac{1}{4} $, w₁ approaches 0, indicating that the interval goes back to the original non-partition interval [0, 1]. If $ \mathrm{c}\ge \frac{1}{4} $, partitioning becomes impossible. On the contrary, if c approaches 0, w₁ reaches $ \frac{1}{2},\kern0.5em $maximizing the information transmission.

Appendix 11.3 Cheap Talk Equilibrium (Numerical Example)

A numerical example of a cheap talk game with two intervals is analyzed when the two intervals represent the smallest partitioning and the least efficient cheap talk equilibrium. (The greater the number of intervals, the more efficient the cheap talk equilibrium.) Thus, it is appropriate to compare the cheap talk game with two intervals and the delegation game analyzed in Appendix 11.4

In a cheap talk game with two intervals, J extends a proposal within each of two intervals (See Fig. 11.1). Basically M knows that J’s proposal has a bias, but uses it to update the prior information and chooses f. M updates its prior belief on w as follows. M knows that w is uniformly distributed between 0 and 1. This prior belief is characterized as the density function h(w) = 1. When J makes a proposal r₁ for the interval w ∈ [0, w₁), M updates its prior belief to the posterior belief h(w| r₁) according to the Bayes theorem as

$$ h\left(w|{\mathrm{r}}_1\right)=\frac{h(w) \Pr \left({r}_1|w\right)}{ \Pr \left(\mathrm{w}\in \left[0,{w}_1\right]\right)} $$

where the prior belief h(w) = 1. Because J always proposes r₁ in the interval, Pr(r₁| w) = 1. Because w is within the interval, Pr(w ∈ [0, w₁]) = w₁. Inserting these into the above equation gives $ h\left(w|{\mathrm{r}}_1\right)=\frac{1}{w_1} $.

Consider M’s choice. When J proposes r₁ in the interval w ∈ [0 , w₁), M chooses f₁ in order to maximize its expected utility. M’s expected utility is given by

$$ {EU}_M^C={\int}_0^{w_1}-{\left({f}_1-w\right)}^2h(w) dw. $$

Solving this yields

$$ {EU}_M^C=-{f}_1^2{w}_1+{f}_1{w}_1^2-\frac{1}{3}{w}_1^3. $$

The first-order condition is $ \frac{dEU_M^C}{d{f}_1}=-2{f}_1+{w}_1=0 $$ {f}_1=\frac{w_1}{2}. $

Likewise, if J proposes r₂ for the interval w ∈ [w₁, 1], M chooses $ {f}_2=\frac{w_1+1}{2} $. As for J’s other proposals in the two intervals, M does not change its posterior beliefs and choices as noted above.

Given M’s responses, J proposes $ {r}_1=\frac{w_1}{2} $ for the interval w ∈ [0 , w₁). J proposes $ {r}_2=\frac{w_1+1}{2} $ for the internal w ∈ [w₁, 1].The stated J’s proposals are equilibrium strategies. For instance, suppose that for the interval w ∈ [0 , w₁), J extends a proposal $ {r}_3=\frac{w_1+1}{2} $. Then M holds the posterior belief (w| r₃)=0 and predicts $ w=\frac{1}{2} $, with the game ending with a babbling equilibrium. Since J’s expected utility in the babbling equilibrium is inferior to that in a cheap talk equilibrium (shown below), J has no incentive to deviate from r₁. A cheap talk equilibrium is a separating equilibrium in the sense that J’s proposal will differ depending on the value of w.

Using these results and Eq. (11.1) in the main text, M’s expected utility can be calculated as

$$ {EU}_M^C={\int}_0^{w_1}{-\left(\,f-w\right)}^2h(w) dw+{\int}_{w_1}^1{-\left(\,f-w\right)}^2h(w) dw, $$

where for w ∈ [0 , w₁), M chooses $ {f}_1=\frac{w_1}{2} $ in response to J’s r₁. In contrast, for w ∈ [w₁, 1], M chooses $ {f}_2=\frac{w_1+1}{2} $ in response to J’s r₂. M’s expected utility can be solved as

$$ {EU}_M^C={\int}_0^{w_1}{-\left(\frac{w_1}{2}-w\right)}^2h(w) dw+{\int}_{w_1}^1{-\left(\frac{w_1+1}{2}-w\right)}^2h(w) dw=-\frac{1}{48}-{c}^2 $$

Using Eq. (11.2) in the main text, J’s expected utility is calculated as

$$ {EU}_J^C=-\frac{1}{48}-2{c}^2 $$

Insofar as $ 0\le \mathrm{c}<\frac{1}{4} $, M’s and J’s expected utilities in the cheap talk equilibrium are greater than those in the babbling equilibrium calculated in Appendix 11.1.

Appendix 11.4 Critical Value for Delegation to the Global Institution

If J delegates to global institution G, M uses G’s proposal r_G to make its institutional choice ( f = w + g). In this case, M’s expected utility is $ {U}_M^D={-g}^2 $, while J’s expected utility is $ {U}_J^D=-{g}^2-{c}^2. $ If J chooses not to delegate, the game is the same as the one analyzed in Appendix 11.3. As argued in the main text, J must decide between delegation and non-delegation. This delegation decision is made based on the following expected utility calculation.

Let $ \overset{-}{g} $ be the critical value for G’s bias. If delegation and J’s utility are equal, $ {U}_J^D=-{\left(g-c\right)}^2 $, but $ {U}_J^C=-\frac{1}{48}-2{c}^2 $ for non-delegation and J uses its own proposal. The critical value $ \overset{-}{g}, $ which is non-negative, is obtained as

$$ \overset{-}{g}=\pm \sqrt{\frac{1}{48}+{2c}^2}+c\kern0.5em \mathrm{for}\ g\gtreqless c. $$

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Globalism and Regionalism: The East Asian Currency Crisis and Institutional Building

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