## Saturday, October 23, 2021

### Swiss Micros DM41X and HP Prime: The Exit Game

Swiss Micros DM41X and HP Prime: The Exit Game

Introduction

We have two entities in an area:  A and B.   Unfortunately, that area isn't big enough for A and B to stay.  If both A and B stay, they suffer a loss (think economical loss, but it can apply to morality loss, emotional loss, etc.).   Neither A nor B want to leave and each of them want their opponent to leave instead.

If A and B both leave, neither have any benefits from staying in the area.

The program EXTGAME/EXITGAME calculates four probabilities:

P(A):  probability A stays if A is indifferent of whether B stays or leaves

K_a =  G_a ÷ (G_a - L_a)

P(B):  probability B stays if B is indifferent of whether A stays or leaves

K_b =  G_b ÷ (G_b - L_b)

P(both):  probability that both A and B stay, given they are indifferent about what their opponent does

P(both) = K_a × K_b

P(neither):  probability that both leave, given they are indifferent about what their opponent does

P(neither) = (1 - K_a) × (1 - K_b)

DM41X Program:  EXTGAME

01 LBL^T EXTGAME

02 ^T A LOSS?

03 PROMPT

04 STO 01

05 ^T A GAIN?

06 PROMPT

07 STO 02

08 ENTER

09 ENTER

10 RCL 01

11 -

12 /

13 STO 05

14 ^T P<A>=

15 ARCL 05

16 AVIEW

17 STOP

18 ^T B LOSS?

19 PROMPT

20 STO 03

21 ^T B GAIN?

22 PROMPT

23 STO 04

24 RCL 04

25 ENTER

26 ENTER

27 RCL 03

28 -

29 /

30 STO 06

31 ^T P<B>=

32 ARCL 06

33 AVIEW

34 STOP

35 RCL 05

36 RCL 06

37 *

38 ^T P<BOTH>=

39 ARCL X

40 AVIEW

41 STOP

42 1

43 RCL 05

44 -

45 1

46 RCL 06

47 -

48 *

49 ^T P<NONE>=

50 ARCL X

51 AVIEW

52 END

HP Prime Program: EXITGAME

EXPORT EXITGAME()

BEGIN

// 2021-07-30 EWS

MSGBOX("Game of Chicken/Exit: Either A

or B must leave or they both lose.");

LOCAL la,lb,ga,gb,ka,kb,m;

INPUT({la,ga},"A is indifferent",

{"Loss/B stays: ",

"Gain/B leaves: "});

INPUT({lb,gb},"B is indifferent",

{"Loss/A stays: ",

"Gain/A leaves: "});

ka:=ga/(ga-la);

kb:=gb/(gb-lb);

m:=[[la,lb,0,gb],[ga,0,0,0]];

PRINT();

PRINT("*** Matrix ***");

PRINT2D(m);

PRINT("*** Results ***");

PRINT("---------------");

PRINT("Prob. A Stays: "+STRING(ka));

PRINT("Prob. B Stays: "+STRING(kb));

PRINT("Prob. Both Stays: "+

STRING(ka*kb));

PRINT("Prob. Both Leave: "+

STRING((1-ka)*(1-kb)));

END;

Example

Example:  For players A and B:

A is indifferent:

A's Loss if B Stays:  -45  (DM41X prompt:  A LOSS?)

A's Gain if B Leaves:  +50 (A GAIN?)

B is indifferent:

B's Loss if A Stays: -35 (B LOSS?)

B's Gain if A Leaves: +60 (B GAIN?)

Results:

Probability A Stays:  0.526315789474  (P<A>)

Probability B Stays:  0.631578947368 (P<B>)

Probability both A and B stay:  0.332409972299 (P<BOTH>)

Probability both A and B leave: 0.174515235457 (P<NONE>)

Source:

Ivan Pastine, Tuvana Pastine, Tom Humberstone.  Introducing Game Theory: A Graphic Guide Icon Books Ltd:  London, United Kingdom.  2017  ISBN 9781785780820

Eddie

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