==============
Part 0: Inputs
==============
 
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0. Config Parameters
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a. Number of actions
 
 NA(1) = 2
 NA(2) = 2
 
b. Number of signals
 
 NY(1) = 2
 NY(2) = 2
 
c. Number of states
 
 NW(1) = 2
 NW(2) = 2
 
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1. Model Parameters
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a. Discount factor
 
 beta = 0.9
 
b. Period payoffs
 
 u1(a1=1,y1=1) = 0.6
 u1(a1=1,y1=2) = -0.4
 u1(a1=2,y1=1) = 1
 u1(a1=2,y1=2) = 0
 
 u2(a2=1,y2=1) = 0.6
 u2(a2=1,y2=2) = -0.4
 u2(a2=2,y2=1) = 1
 u2(a2=2,y2=2) = 0
 
c. Signal probabilities
 
 P(y1=1,y2=1|a1=1,a2=1) = 0.8556
 P(y1=1,y2=2|a1=1,a2=1) = 0.0244
 P(y1=2,y2=1|a1=1,a2=1) = 0.0244
 P(y1=2,y2=2|a1=1,a2=1) = 0.0956
 
 P(y1=1,y2=1|a1=1,a2=2) = 0.5231
 P(y1=1,y2=2|a1=1,a2=2) = 0.0244
 P(y1=2,y2=1|a1=1,a2=2) = 0.0244
 P(y1=2,y2=2|a1=1,a2=2) = 0.4281
 
 P(y1=1,y2=1|a1=2,a2=1) = 0.5231
 P(y1=1,y2=2|a1=2,a2=1) = 0.0244
 P(y1=2,y2=1|a1=2,a2=1) = 0.0244
 P(y1=2,y2=2|a1=2,a2=1) = 0.4281
 
 P(y1=1,y2=1|a1=2,a2=2) = 0.2856
 P(y1=1,y2=2|a1=2,a2=2) = 0.0244
 P(y1=2,y2=1|a1=2,a2=2) = 0.0244
 P(y1=2,y2=2|a1=2,a2=2) = 0.6656
 
d. Correlation device
 
 x(s1=1,s2=1) = 0.25
 x(s1=1,s2=2) = 0.25
 x(s1=2,s2=1) = 0.25
 x(s1=2,s2=2) = 0.25
 
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2. Strategy Parameters
----------------------
 
a. Action probabilities
 
 p1(a1=1|w1=1) = 1
 p1(a1=2|w1=1) = 0
 p1(a1=1|w1=2) = 0
 p1(a1=2|w1=2) = 1
 
 p2(a2=1|w2=1) = 1
 p2(a2=2|w2=1) = 0
 p2(a2=1|w2=2) = 0
 p2(a2=2|w2=2) = 1
 
b. State transition rules
 
 w1+(w1=1,a1=1,y1=1) = 1
 w1+(w1=1,a1=1,y1=2) = 2
 w1+(w1=1,a1=2,y1=1) = 1
 w1+(w1=1,a1=2,y1=2) = 2
 
 w1+(w1=2,a1=1,y1=1) = 1
 w1+(w1=2,a1=1,y1=2) = 2
 w1+(w1=2,a1=2,y1=1) = 1
 w1+(w1=2,a1=2,y1=2) = 2
 
 w2+(w2=1,a2=1,y2=1) = 1
 w2+(w2=1,a2=1,y2=2) = 2
 w2+(w2=1,a2=2,y2=1) = 1
 w2+(w2=1,a2=2,y2=2) = 2
 
 w2+(w2=2,a2=1,y2=1) = 1
 w2+(w2=2,a2=1,y2=2) = 2
 w2+(w2=2,a2=2,y2=1) = 1
 w2+(w2=2,a2=2,y2=2) = 2
 
c. Initial states
 
 w_{0,1}(s1=1) = 1
 w_{0,1}(s1=2) = 2
 
 w_{0,2}(s2=1) = 1
 w_{0,2}(s2=2) = 2
 
========================================================
Part I: Is the strategy's behavior consistent with CSE?
        -- Evaluation based on Mbar
========================================================
 
1. The relevant belief sets are:
 
 Mbar_1(w1=1) = convex hull of the following 2 extreme points:
 (1) 0.9234     0.0766
 (2) 0.9720     0.0280
 
 Mbar_1(w1=2) = convex hull of the following 2 extreme points:
 (1) 0.0358     0.9642
 (2) 0.1887     0.8113
 
 
 Mbar_2(w2=1) = convex hull of the following 2 extreme points:
 (1) 0.9234     0.0766
 (2) 0.9720     0.0280
 
 Mbar_2(w2=2) = convex hull of the following 2 extreme points:
 (1) 0.0358     0.9642
 (2) 0.1887     0.8113
 
 
2. Evaluation of incentives:
 
 All incentives hold.
 
=========================================================
Part II: Is the strategy's behavior consistent with CSE?
         -- Evaluation based on M_pi^*
=========================================================
 
There are 1 stationary state distributions.
Their values and associated results are the following:
 
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Results from stationary distribution # 1
----------------------------------------
 
0. The stationary distribution pi is:
 
 pi(w1=1,w2=1) = 0.69114
 pi(w1=1,w2=2) = 0.0244
 pi(w1=2,w2=1) = 0.0244
 pi(w1=2,w2=2) = 0.26006
 
1. The relevant belief sets are:
 
 M_pi^*_1(w1=1) = convex hull of the following 2 extreme points:
 (1) 0.9234     0.0766
 (2) 0.9720     0.0280
 
 M_pi^*_1(w1=2) = convex hull of the following 2 extreme points:
 (1) 0.0358     0.9642
 (2) 0.1887     0.8113
 
 
 M_pi^*_2(w2=1) = convex hull of the following 2 extreme points:
 (1) 0.9234     0.0766
 (2) 0.9720     0.0280
 
 M_pi^*_2(w2=2) = convex hull of the following 2 extreme points:
 (1) 0.0358     0.9642
 (2) 0.1887     0.8113
 
 
2. Evaluation of incentives:
 
 All incentives hold.
 
===============================================================
Part III: Is (x,sigma) a CSE?
          -- Evaluation using user-supplied starting conditions
===============================================================
 
1. The relevant belief sets are:
 
 M^{U*}_1(w1=1) = convex hull of the following 2 extreme points:
 (1) 0.5000     0.5000
 (2) 0.9720     0.0280
 
 M^{U*}_1(w1=2) = convex hull of the following 2 extreme points:
 (1) 0.0358     0.9642
 (2) 0.5000     0.5000
 
 
 M^{U*}_2(w2=1) = convex hull of the following 2 extreme points:
 (1) 0.5000     0.5000
 (2) 0.9720     0.0280
 
 M^{U*}_2(w2=2) = convex hull of the following 2 extreme points:
 (1) 0.0358     0.9642
 (2) 0.5000     0.5000
 
 
2. Evaluation of incentives:
 
 Player 1 has the incentive to deviate to a1=2 in state w1=1
 when his belief is extreme point (1) in M^{U*}_1
 
 Player 2 has the incentive to deviate to a2=2 in state w2=1
 when his belief is extreme point (1) in M^{U*}_2
 
==================================================================
Part IV: Is (x,sigma) a CSE?
         -- Evaluation using all deterministic starting conditions
==================================================================
------------------------------------------
Results for (w_{0,1},w_{0,2})=(1,1) w.p. 1
------------------------------------------
 
1. The relevant belief sets are:
 
 M^{U*}_1(w1=1) = convex hull of the following 2 extreme points:
 (1) 0.9234     0.0766
 (2) 1.0000     0.0000
 
 M^{U*}_1(w1=2) = convex hull of the following 2 extreme points:
 (1) 0.0358     0.9642
 (2) 0.2033     0.7967
 
 
 M^{U*}_2(w2=1) = convex hull of the following 2 extreme points:
 (1) 0.9234     0.0766
 (2) 1.0000     0.0000
 
 M^{U*}_2(w2=2) = convex hull of the following 2 extreme points:
 (1) 0.0358     0.9642
 (2) 0.2033     0.7967
 
 
2. Evaluation of incentives:
 
 All incentives hold.
 
------------------------------------------
Results for (w_{0,1},w_{0,2})=(1,2) w.p. 1
------------------------------------------
 
1. The relevant belief sets are:
 
 M^{U*}_1(w1=1) = convex hull of the following 2 extreme points:
 (1) 0.0000     1.0000
 (2) 0.9720     0.0280
 
 M^{U*}_1(w1=2) = convex hull of the following 2 extreme points:
 (1) 0.0354     0.9646
 (2) 0.1887     0.8113
 
 
 M^{U*}_2(w2=1) = convex hull of the following 2 extreme points:
 (1) 0.9234     0.0766
 (2) 0.9723     0.0277
 
 M^{U*}_2(w2=2) = convex hull of the following 2 extreme points:
 (1) 0.0358     0.9642
 (2) 1.0000     0.0000
 
 
2. Evaluation of incentives:
 
 Player 1 has the incentive to deviate to a1=2 in state w1=1
 when his belief is extreme point (1) in M^{U*}_1
 
 Player 2 has the incentive to deviate to a2=1 in state w2=2
 when his belief is extreme point (2) in M^{U*}_2
 
------------------------------------------
Results for (w_{0,1},w_{0,2})=(2,1) w.p. 1
------------------------------------------
 
1. The relevant belief sets are:
 
 M^{U*}_1(w1=1) = convex hull of the following 2 extreme points:
 (1) 0.9234     0.0766
 (2) 0.9723     0.0277
 
 M^{U*}_1(w1=2) = convex hull of the following 2 extreme points:
 (1) 0.0358     0.9642
 (2) 1.0000     0.0000
 
 
 M^{U*}_2(w2=1) = convex hull of the following 2 extreme points:
 (1) 0.0000     1.0000
 (2) 0.9720     0.0280
 
 M^{U*}_2(w2=2) = convex hull of the following 2 extreme points:
 (1) 0.0354     0.9646
 (2) 0.1887     0.8113
 
 
2. Evaluation of incentives:
 
 Player 1 has the incentive to deviate to a1=1 in state w1=2
 when his belief is extreme point (2) in M^{U*}_1
 
 Player 2 has the incentive to deviate to a2=2 in state w2=1
 when his belief is extreme point (1) in M^{U*}_2
 
------------------------------------------
Results for (w_{0,1},w_{0,2})=(2,2) w.p. 1
------------------------------------------
 
1. The relevant belief sets are:
 
 M^{U*}_1(w1=1) = convex hull of the following 2 extreme points:
 (1) 0.9213     0.0787
 (2) 0.9720     0.0280
 
 M^{U*}_1(w1=2) = convex hull of the following 2 extreme points:
 (1) 0.0000     1.0000
 (2) 0.1887     0.8113
 
 
 M^{U*}_2(w2=1) = convex hull of the following 2 extreme points:
 (1) 0.9213     0.0787
 (2) 0.9720     0.0280
 
 M^{U*}_2(w2=2) = convex hull of the following 2 extreme points:
 (1) 0.0000     1.0000
 (2) 0.1887     0.8113
 
 
2. Evaluation of incentives:
 
 All incentives hold.
 
