FINITE GAMES

A Players B Players

No of Observations O: 280 *No of Observations O: 275

No. of No. ofAll Machines Fitness % of O All Machines Fitness % of O1 state 2 70 25.0% 1 state 2 142 51.6%2 state 12 171 61.1% 2 state 26 174 63.3%3 state 176 206 73.6% 3 state 1054 208 75.6%

1 state + 10 255 91.1% 1 state + 10 265 96.4%2 state + 18 256 91.4% 2 state + 32 268 97.5%3 state + 180 278 99.3% 3 state + 1058 274 99.6%

No. in Fitness of Best Fitting Sets from: No. in Fitness of Best Fitting Sets from: Bn 1 2 3 1 + 2 + 3 + Bn 1 2 3 1 + 2 + 3 +1 65 145 145 145 145 145 1 121 124 126 124 124 1262 70 156 169 197 197 205 2 142 153 157 168 168 1713 n.a. 162 182 227 227 239 3 N/A 172 183 196 196 1994 n.a. 167 189 239 239 253 4 N/A 174 203 222 223 2255 n.a. 170 194 245 245 259 5 N/A 174 205 246 247 2496 n.a. 171 197 250 250 264 6 N/A 174 206 265 266 269

*Note - Five observations are missing since the A Player did not send for five entire supergames

INDEFINITE GAMES

A Players B Players

No of Observations O: 280 No of Observations O: 280

No. of No. ofAll Machines Fitness % of O All Machines Fitness % of O1 state 2 170 60.7% 1 state 2 187 66.8%2 state 12 227 81.1% 2 state 26 225 80.4%3 state 176 249 88.9% 3 state 1054 244 87.1%

1 state + 10 224 80.0% 1 state + 10 240 85.7%2 state + 18 237 84.6% 2 state + 32 251 89.6%3 state + 180 255 91.1% 3 state + 1058 261 93.2%

No. in Fitness of Best Fitting Sets from: No. in Fitness of Best Fitting Sets from: Bn 1 2 3 1 + 2 + 3 + Bn 1 2 3 1 + 2 + 3 +1 170 202 202 193 202 202 1 158 161 162 161 161 1622 170 211 212 206 211 212 2 187 192 194 188 192 1943 n.a. 218 222 213 218 222 3 n.a. 212 218 208 212 2184 n.a. 222 227 216 222 227 4 n.a. 217 230 221 224 2315 n.a. 224 231 218 225 231 5 n.a. 221 237 230 233 2436 n.a. 226 235 220 227 237 6 n.a. 222 240 236 239 249

Table 1: Fitness of All and Best Fitting Machines in the Training Sample

Training Sample Test SampleUnique Total Unique Total

Machine Fitness Fitness Fitness Fitness

Ma15 20% 40% 15% 42%Finite Player A Ma14 17% 38% 8% 35%

Ma1 23% 23% 9% 9%

Mb1 20% 44% 12% 29%Finite Player B Mb28 15% 41% 13% 43%

Mb27 10% 19% 17% 38%

Indef. Player A Ma3 72% 72% 67% 67%

Mb6 43% 57% 32% 46%Indef. Player B Mb11 7% 22% 5% 21%

Mb25 11% 11% 15% 17%

Table 2: Inferred Strategies and Their Fitness

1. Based on c = 5% threshold

FIRST TEN SUPERGAMES LAST TEN SUPERGAMES

Training Sample Test Sample Training Sample Test SampleUnique Total Unique Total Unique Total Unique Total

Machine Fitness Fitness Fitness Fitness Machine Fitness Fitness Fitness Fitness

Ma15 28% 42% 21% 47%Finite Player A Ma14 15% 29% 10% 36% Ma15 46% 46% 34% 34%

Ma1 26% 26% 13% 13% Ma5 27% 27% 6% 6%

Mb1 24% 43% 15% 31% Mb30 41% 46% 25% 34%Finite Player B Mb28 20% 42% 18% 44% Mb7 17% 21% 7% 15%

Mb27 11% 17% 15% 30%

Indef. Player A Ma3 67% 67% 62% 62% Ma3 77% 77% 71% 71%

Mb6 54% 54% 62% 62% Mb6 28% 61% 17% 55%Indef. Player B Mb16 14% 14% 20% 20% Mb24 9% 9% 13% 15%

Mb28 9% 42% 11% 51%

1. Based on c = 5% threshold2. Arrows reflect similar machines that they have almost identical structure accept for one or two transitions

Table 3: Inferred Strategies and Their Fitness Over Time

Figure 1: Trust Game Extensive Form

Keep

Player A

A: 0 B: 120

A: 40

B: 40 Return

Don’t Send Send

Player B

A: 60

B: 60

Keep

Figure 2: Player A, Set s ≤ 2 MA1 MA2 MA3 MA4 MA5 MA6 MA7 MA8 MA9 MA10 MA11 MA12

S

R, K

S DR, K

K, R D S

S D R K

K S DR

D S K, R

D S K R

S D

R K

D

R, K

D S K

R

K S D

R R, K S D

Figure 3: Player B, Set s ≤ 2 MB1 MB2 MB3 MB4 MB5 MB6 MB7 MB8 MB9 MB10 MB11 MB12 MB13 MB14

MB15 MB16

MB17 MB18

MB19 MB20

MB21 MB22

MB23 MB24

MB25 MB26

R

S, D K

S, D

D R KS S, D

R KS SD

D

R KS D D

S

R K S D S, D

R KS D

S, D

R KD SD

D

R KD D S

S

R KSS, D

D S, D R K

S, D

R KD S

S, D

R KD S, D

S R KS, D

S, D

D K R S S, D

K R S D D

S

K R S D S, D

K R D D S

S

S, K R S, D

K R D S, D

S

K R S SD

D

K R S D

S, D

K R D SD

D

K R SS, D

D

K R D S

S, D

K R S, D

S, D

Figure 4: Player A, Set “+”

K

DSR R, K

S

DS SKR R R, K

S

K

SS S DSK K

SR R R R, K

K

D

S DR, K

SD D DDSKR

D DDK

SR

DDK

SR

S

R, K K S D

R

MA2 MA4

MA13

MA14

MA15

MA1 MA5

MA16

MA17

MA18

End Game Effect Strategies

Punishment Strategies

Figure 5: Player B, Set “+”

SR R KRD D

RS S S S, D

D S, D

R KRDS S S, D

R

D S, D

KRS S, D

R

D S, D

K S, D R KS, D

End Game Effect Strategies

MB2 MB11

MB27

MB28

MB29

KKD

RS S, D

S, D

K KKD

RS S, D S, D

S, D

SK K KKRDS S, D S, D S, D

S, D

R

S, DR K

S D

S, D

Punishment Strategies

MB1 MB6

MB30

MB31

MB32

Player A Player B

Player A Player B

R KRDS S S, D

R

D S, D

KRS S, D

R

D S, D

KS DR

R KS D

S, D

S, DR KS, D

K RDS, D

S

Figure 6a: Inferred Strategies In All Finite Supergames

Mb1

Mb28

Mb27

Figure 6b: Inferred Strategies In All Indefinite Supergames

Mb6

Ma15

Ma14

Ma1

Ma3

Mb11

Mb25

R

S, D

S

R, K

DS SK R R R, K

S

K

S S DSK K

SR R R R, K

K

Player B: Last 10 Supergames Player B: First 10 Supergames

Player A: Last 10 Supergames Player A: First 10 Supergames

R KRD S S S, D

R

D S, D

KRS S, D

R

D S, D

Figure 7a: Inferred Player A Strategies In Finite Supergames

Mb1

Mb28

Mb27

Figure 7b: Inferred Player B Strategies In Finite Supergames

Mb30

Ma15

Ma14

Ma1

Mb7

R

S, D

S

R, K

DS SK R R R, K

S

K

S S DSK K

SR R R R, K

K

Ma14 DS SKR R R, K

S

K

KKD

RS S, D

S, D

R KSD S, D

Ma5 KS D

R

Player B: Last 10 Supergames Player B: First 10 Supergames

Player A: Last 10 Supergames Player A: First 10 Supergames

R KRDS S S, D

R

D S, D

Figure 8a: Inferred Player A Strategies In Indefinite S

Mb6

Mb16

Figure 8b: Inferred Player B Strategies In Indefinite S

Ma3 KS DR

R KS D

S, D

K R S SD

D K RSS, D

D

Mb6 R K

S D

S, D

Mb24

Mb28

Ma3 KS DR