**4. Results**

The raw data are available upon request from the author. In what follows, we use non-parametric tests and logistic regressions in order to analyze our results.<sup>4</sup>

#### **4.1 Some general considerations about individuals' behavior**

#### *4.1.1 Existence of threshold strategies*

According to Heinemann et al. [2], the behavior is consistent with undominated strategy if this behavior, during a period, is consistent with the existence of thresholds.

In other terms,


<sup>3</sup> See Appendix C.

<sup>4</sup> All tables and figures related to our results are available in Appendix D.

**Figure 1** displays the number of cases where subjects played undominated strategies. This is very predominant especially in the sixth and twelfth periods, with 65 and 62 cases in total, respectively. More generally, a threshold strategy means that subjects were not able to predict sometimes others' choices.

Although signals differ in nature (public versus private), different interpretations of public information lead somewhat to this common information to be a private one. Consequently, common information does not lead necessarily to common knowledge. In other terms, different interpretations of public information are considered also as private ones.

Given the fact that the number of players is low, the level of reasoning of players increases sometimes but with strategies change.

#### *4.1.2 The determinant signal of individual behavior*

We estimate the probability with which a subject chooses B by fitting a logistic distribution function to observed choices. The cumulative logistic distribution is given by:

$$P(B) = \frac{1}{1 + \exp\left(-a - bPr - cPu\right)}$$

We analyse whether the public signal is used as a focal point by the subjects. We define the null hypothesis as follows:

H0: the weight assigned to the public signal (c) is not different from the weight assigned to the private signal (b).

We test H0 owing to a Wilcoxon matched pairs signed rank test and both of them allowed us to derive these observations:

• Players seem to be indifferent between the two types of signals. P-value is equal to 0.9594. So, there is no evidence of using public information as a focal point by the agents. In other terms, subjects give equal weights to both signals (cf. **Table 3**).

#### **4.2 The threshold to successful attacks**

Players have a tendency to choose the safe action (A) for low values of Y and to decide on the risky action (B) for higher values of Y (cf. **Figure 2**).

**Table 4** gives an indication on states in which B was a successful strategy. We define the interval of indeterminacy; whose lower bound is the lowest value of Y and above which the attack is successful, and whose upper bound is the highest value of Y until which B fails. The middle point of that interval gives information about the probability of a successful attack and the amplitude of this interval indicates the predictability of a successful attack.

#### **4.3 Probability and the predictability of a speculative attack**

#### *4.3.1 The aggregate behavior analysis*

#### *4.3.1.1 Probability of a successful attack*

**Table 5** displays some statistics relative to the probability and the predictability of an attack. The mean threshold to success, as well as the average width of an interval of *Central Bank Transparency and Speculative Attacks: An Overview and Insights from… DOI: http://dx.doi.org/10.5772/intechopen.107247*

indeterminacy, is higher when the gain associated with the safe action increases (T = 50). That observation coincides with OLS estimations.<sup>5</sup> We tested the impact of control variables (cf. **Table 6** for description and definition of data) on mean thresholds Y\* through linear regression (Eq. 1).

$$Y\_i^\* = \gamma\_0 + \gamma\_1 T\_i + \gamma\_2 Ord\_i + \gamma\_3 TO\_i + u\_i \tag{1}$$

Y\* is the threshold state that characterizes the behavior of a player (an agent) who attacks if he/she "*gets a signal above this threshold, and does not attack otherwise*" ([7], p.2). The payoff associated with the safe action T has a significant and positive impact on the probability of an attack. Order (Ord) adds a high and significant value to the level of threshold. An interaction term is used to control for nonlinearity in the payoff function. The variable TO is included to capture the different sizes of the order effect in the two stages. It is negative but insignificant. Overall, the controls explain about 89% of the total regression.

### *4.3.1.2 Predictability of an attack*

We regress the interval that separates between the highest state up to which action B always failed and the lowest state from which action B was always successful (Δ*Y* <sup>∗</sup> ) on some controls.

$$
\Delta Y\_i^\* = \chi\_0 + \chi\_1 T\_i + \chi\_2 Ord\_i + \chi\_3 T O\_i + u\_i \tag{2}
$$

Eq. (3) in **Table 7** shows that only order variable (Ord) has a significant impact onΔ*Y* <sup>∗</sup> .

### *4.3.2 The individual behavior analysis*

The results of individual behavior analysis are in accordance with those of aggregate behavior. We estimate the proportion of agents who choose a risky action B by using a logistic estimation, for each session as follows:

To estimate the probability of choosing an action B, we use a logit model:

$$P(De) = \frac{1}{1 + \exp\left(-De\right)}$$

The relationship between De and the independent variables is supposed to be linear:

*De* ¼ *a* þ *b Pr* þ *c Pu* þ *u*,*u* is the error term

Mean ¼ �*a=*ð Þ *<sup>b</sup>* <sup>þ</sup> *<sup>c</sup>* and standard deviation <sup>¼</sup> *<sup>π</sup>=*ð Þ *<sup>b</sup>* <sup>þ</sup> *<sup>c</sup>* ffiffiffi 3 <sup>p</sup> *:*

The mean of the function (�*a=*ð Þ *b* þ *c* ) is an indication of the probability of an attack and its standard deviation (*π=*ð Þ *<sup>b</sup>* <sup>þ</sup> *<sup>c</sup>* ffiffiffi <sup>3</sup> <sup>p</sup> ) measures the predictability of a speculative attack (cf. **Table 8**).

The **results** can be interpreted in two ways:

<sup>5</sup> Following Heinemann et al. [2], as the individual behavior does not change after the first periods, we combine data of the last four periods in order to improve the quality of the estimates.


As in our previous findings, the mean of thresholds is higher when T = 50 (cf. **Table 9**), but the standard deviation of thresholds is lower when the payoff is lower.

#### *4.3.2.1 Probability of a successful attack*

Eq. (3) estimates the effect of control variables on the estimated mean threshold.

$$-a/(b+c) = \chi\_0 + \chi\_1 T\_i + \chi\_2 Ord\_i + \chi\_3 T O\_i + u\_i \tag{3}$$

The payoff of the secure action contributes significantly and positively to the estimated mean threshold. The result is in accordance with the preliminary analysis following **Table 9**. Order effect is negative and significant. The interaction term (TO) is, however, insignificant.

#### *4.3.2.2 Predictability of an attack*

It is clear that the average standard deviation is always higher when the payoff of the secure action is high.

$$
\pi/(b+c)\sqrt{3} = \chi\_0 + \chi\_1 T\_i + \chi\_2 Ord\_i + \chi\_3 T O\_i + \mu\_i \tag{4}
$$

Eq. (4) shows that this is indeed significant only at 10%. The interaction term (TO) regains its significance but the order variable (Ord) turns out to be insignificant although it has its expected sign.

### **4.4 Coordination failure**

In this section, we study the impact of the informational structure on coordination. We distinguish two extreme cases: Perfect coordination versus total coordination failure.

We define perfect coordination as the situation in which all agents choose the same action. Total coordination failure is the situation in which two players choose the same action. There are a total of 494 cases where subjects played the same action (cf. **Table 10**).<sup>6</sup> Following Cornand [5], a deep interpretation of the coordination concept can be observed through a measure of the former (i.e., number of regrettable decisions). Indeed, when individual behavior fails, this means that the subject had difficulty in interpreting the signals he/she received. Therefore, he/she was unable to predict whether an attack was successful or not. This can happen in two situations:


<sup>6</sup> Total number of situations = 10\*16\*5 = 800.

*Central Bank Transparency and Speculative Attacks: An Overview and Insights from… DOI: http://dx.doi.org/10.5772/intechopen.107247*

We proceed to calculate the number of regrettable decisions (the player regrets his choice according to the situations described above). **Figure 3** shows that this number is particularly high in the first periods (periods 2 and 3) of stage 1. The number of regrettable decisions decreases over the following periods and regains a higher peak though a bit lower than in periods 2 and 3 at the end of stage 1 (period 8). Overall, the number of regrettable decisions clearly decreases in stage 2.
