Chapter 2 A Regime Change Model with Speculators and Stakeholders
2.1 Introduction
A regime in this work refers to the set of social rules and and norms that depict the form of a government. (1) It can change for both internal and external reasons. For the former, we have seen political changes such as the collapse of the Soviet Union, the reform of China since 1978, the Arab spring revolutions, and the recently approved Obamacare, in which the pressures for regime changes came mainly from the inside participants, i. e. , the citizens, of the regime. The latter cases refer to regime changes that happen mainly because of outside interferences, such as the collapses of the Taliban regime in Afghanistan and the Saddam regime in Iraq. In this work, we ignore external aspects and focus on regime changes with internal pressures.
Once a regime has been chosen for a society, each individual in it gets her payoff according to her behavior as well as the distribution rules embedded in the regime. That explains why there may exist internal pressures for a regime change: If an individual believes she can better off by successfully attacking the current regime, she may have the incentive to do so. But even if the payoff after the regime change is higher, attacking the status quo involves two kinds of costs. The first one is the attacking cost measuring the opportunity cost of attacking. The second one is the cost of risk, which occurs because of the possibility of an unsuccessful attack. Usually a significantly large number of attacking individuals is required to make a regime change happen, so a single individual's payoff on attacking depends also on others' actions and strategic supermodularities exist here: The greater the fraction of other attacking individuals, the smaller the cost of risk for an individual to attack. A rational individual must take into account the trade-off between potential gains and underlying risks while making her decision on whether or not to attack the current regime.
In any given regime, it is usually the case that some individuals benefit more from the underlying distribution rules and others who benefit less or are even harmed, are taken advantage of to support the regime. In other words, we have different social classes within the regime. Individuals in the upper classes, the stakeholders, can enjoy their vested interests as long as the regime remains. For this reason, stakeholders may be less willing to attack the current regime compared to others. What is more, individuals usually make their decisions repeatedly in reality and their labels could be changed because of their actions in previous stages. This could happen because of the authority's effort to stabilize the current regime: It punishes stakeholders who attacked the regime by kicking them out of the interest group, or rewards previous supporters by absorbing them into the interest group and they can thus enjoy vested interests in the future. Although these two strategies have been widely observed and rigorously used by the authority whenever a regime was about to happen, e. g. , right before the collapses of Chinese dynasties over the last 3000 years, differences in their functions haven't been checked formally yet. The current work addresses this concern based on global game models that are suitable to the economic contexts of interest as depicted above.
A global game is an incomplete information game in which the payoff structure is indexed by some unobservable fundamental random variables. The players can only observe private signals of the realization of the fundamental with noises. After observing their signals, players must take into account all possibilities of payoff structures based on their posterior distributions of the fundamental variable. Carlsson and van Damme (1993) first define and investigate the general two-by-two global games, their motivation is related to that of Rubinstein's (1989) electronic mail game: For a game admitting multiple equilibria under complete information, how will the equilibrium structure change if we disturb the game a little such that the resulting incomplete information game is arbitrarily close to the complete information one? Their result is striking: It is found that a two-by-two global game essentially admits a unique equilibrium as the noises vanish, and the particular unique equilibrium is independent of the distributions of noises. Furthermore, the uniquely selected equilibrium conforms to the risk dominance criterion of two-by-two game as in Harsanyi and Selten (1988).Frankel, Morris and Pauzner (2003) extend the initial two-by-two model to general global games with strategic complementarities. Morris and Shin (1998, 2000, 2003) initiate the application of global games to currency attack problems, where a continuum of players and a binary action set are usually assumed. With the existence of private signals, the uniqueness property is obtained and a regime change is due to a critical change in the fundamental. (2) It is thus beneficial for players to avoid the miscoordination problem, and for the government to set optimal policy through comparative static analysis. Morris and Shin's approach has become a benchmark model in the literature of global games as well as regime change models, for both theoretical and applied studies.
This work first investigates a static model by dividing the continuum of players into two groups: the traditional speculator group and the stakeholder group. The stakeholder group is defined as a group of players who can get extra payoffs if they refrain from attacking the status quo and the regime change does not happen in the end. This distinction between the two groups is based on the observation of the existence of stakeholders in reality as discussed above. It is found that the partition of the set of players does not change the classical uniqueness property of static global games, although speculators behave differently from the stakeholders in the unique equilibrium because of differences in their payoff settings.
The static game is then extended to two-stage games that allow for different relabeling schemes. Under dynamic settings, it is shown that we may gain multiplicity again with the existence of relabeling mechanisms. Moreover, absorbing speculators makes the current regime more stable in the whole game. In contrast, although kicking out stakeholders makes the regime less vulnerable in the first stage compared to the static case, it may make the vulnerability of the regime rather higher in the second stage. To avoid this policy trap, it is crucial to remain all non-attacking stakeholders in the vested interest group in the second stage.
The rest of the work is organized as follows. Section 2.2 defines the static global game with speculators and stakeholders. Section 2.3 defines the solution concept and characterizes the unique equilibrium of the static game. Comparative static analyses based on the uniqueness are conducted in section 2.4.Section 2.5 extends the static game to a general two-stage game that allows for a variety of relabeling mechanisms. In section 2.6, we introduce several relabeling mechanisms aiming to stabilize the current regime and investigate their effects on the equilibrium results. Section 2.7 concludes.