Friday, December 08, 2006

A Game Theoritic Analysis of Polygyny

by Berly

We will discuss the current hot topic in Indonesia (Hollywood already has a TV series onthe topic since early this year) in economics context. I will employ game theory as tool of analysis since it involves strategic interaction and the payoff depend on other people’s response. (for quick review click here)

The etymologically correct term is polygyny since polygamy is the case with multiple spouses for both genders (the term for one woman with many husband is polyandry).

Let lay out the assumptions. I assume common knowledge (structure and payoff) and reveal preference (the husband will tell truthfully whether he wants poliginy and the wife will tell truthfully whether she accept it or not).

I don’t know how to draw the game tree in blogspot so verbal description should do.

It is a two stage game where on the first stage the husband decides whether to do polygyny and tell his wife. I will only discuss the case of husband with poligyny inclination since otherwise nothing happened and the couple stay monogamous. On the second stage the wife decide whether to accept her husband intention to do polygyny or not.

For husband the preference in descending order is polygyny, monogamiy (with first wife) and divorce first wife to marry the incoming woman (before receiving complains, this condition not apply to all men/husbands). I will discuss the wife's preference a bit later.

Since the husband strictly prefer polygyny to divorcing the first wife to marry the incoming woman then the first wife could threat for divorce if she don’t want poligyny. The husband cancels his intention and they stay monogamous.

Why this is not always the case? The threat is not credible if the husband know the first wife’s preference is (in descending order) monogamous, polygyny & divorce. Meaning the husband know the wife in the end will choose to accept the second marriage than get divorce and be a widow.

The financial struggle of non-working women to get new job after long unemployed is an uphill struggle. There is also problem of society looking down on widows and the difficulty to get new husband after divorce.

First wife everywhere! You can, paradoxically, prevent your husband (if he has the inclination) from conducting polygyny by credibly demonstrating your willingness to divorce him.

So get a good job with decent salary, keep the social network (in case you need better job/ husband) and staybeautiful. You will keep your husband of yourself as long as you want him (caveat, if the assumptions used above are applicable in your case).

More economics of polygyny by our Anglo-Saxon friends here (I also recommend this and this movie for weekend).


Ari Juliano Gema said...

Halo Berly,

Jadi kesimpulannya, para wanita disuruh mempersiapkan kemampuan finansial dulu buat memperkuat bargaining position kalo suaminya minta ijin buat poligami, ya?

BTW, Ini Berly FEUI '95 bukan? Kalo bener, ini Ajo FHUI '94 yang dulu pernah sama2 aktif di Himpunan.

pelantjong maja said...

himpunan apa nih? himpunan mencari istri ya.. hehehhe *kidding

Berly said...

Halo Ajo,

Yup, ini Berly FE'95. Gimana kabar? Skr di AHP yach? Salam buat Ade dan Reva. Baru menengok LegalMinded (formerly known as fiat justitia ruat coelum) minggu lalu.

I will continue in English since not all of our readers understand Indonesian.

The case discussed is (and limited to) where the husband is (or suspected to be) inclined toward polygyny but would not continue if the wife prefer to get divorced than allowing the second marriage to take place.

Otherwise the couple will stay together or there is nothing the wife can do to stop the second marriage (if the first wife refuse, the husband will divorce her anyway).

When limitations above applied, the wife can pre-empt and prevent the husband to start the steps toward poligyny by strengthening her survival potential outside the marriage. The husband then will realize that she can credibly choose divorce than polygyny and stay monogamous.

It applied even when the husband has not ask for permission for the second marriage (actually it work best when the first wife has strong bargaining position since beginning of the marriage or even before).

The paradox of the analysis (John Nash is a genius indeed) is the wife has stronger chance to keep his husband when she can demonstrate that she is willing to loose him and able to live without him.

The other side of analysis is when the first wife can not credibly threaten to get divorce to stop the second wedding, the setting will be altered to repeated games and the husband know that he can get the first wife to agree with the third (and fourth) wife.

I don’t know much about the legal process of poligyny in Indonesia though. Maybe you can enlighten me whether any of it will altered the analysis.

Pelantjong Matja that have found his wife through himpunan (remember that we go together to LK II in Jogja) will see her again soon. Don’t forget to let her read this article :-D

Anonymous said...

First of all I would like to introduce myself, even though some of you might already know about me. My name is Martin Daniel SIYARANAMUAL, right now I am a student at MPSE (Midi-Pyrénées Science Economiques), University of Toulouse 1.
It is quite interesting talking about polygyny/polygamy with game theory approaches. I have several remarks about this stuff. First remark, since this is 2 stage game, where the husband makes his moves first, and according to what Berly have said, that the husband strictly prefer to do the polygamy, then the nash equilibrium either (Polygamy, Accepting) or (polygamy, Refusing). In other words there is nothing that wife can do to avoid the polygamy. For conclusion, I need more explanations about this statement:
"The paradox of the analysis (John Nash is a genius indeed) is the wife has stronger chance to keep his husband when she can demonstrate that she is willing to loose him and able to live without him."
Second remark, Let say the wife will choose refusing as her strategy when her husband asks her about doing polygamy. But still, it doesnt make any change, refer to nash equilibrium, the player only cares about strategy that will gives her/him better utility regardless what other player does. In order to be clear:
Husband has 2 strategies, Monogamy or Polygamy. If he chooses Monogamy, then the game is finish and the utility of both player is (X1, Y1) where X for husband and Y for wife. But, if husband chooses Polygamy, then the game will continue to the second stage, where now is the wife's turn. She can chooses either refusing or accepting her husband proposal. (Polygamy, Refusing)=(X2, Y2) & (Polygamy, Accepting)=(X3, Y3).
Just like I mentioned before, Berly said that the husband strictly prefer polygamy, and then it is obvious that monogamy is dominated strategy.


Berly said...

Hi Martin

Thanks for stopping by on this site, we should definitely plan a rendezvous up since we both in Europe.

I wrote this while keeping in mind not all readers has take a course in game theory (plus I don’t know how to make payoff table in blogger).

Since it is clear that you already well versed in game theory, here is the more rigorous exposition:

On first stage, husband chooses between Polygyny or not. On second stage the wife choose whether to accept or reject. To reject mean getting a divorce

I limited the study where the husband get highest payoff on (Polygyny, accept), lower on (not polygyny) and lowest on (polygyny, reject). The last one means monogyny with new wife after divorcing the old wife.

The wife payoff (credibly communicated to husband) is highest on (not polygyny), lower on (polygyny, reject) and lowest on (Polygyny, accept).

Just insert numbers fulfilling preference relations (ex: 1,2,3) and use standard backward induction, the Nash Sub-game Perfect Nash Equilibrium will be non polygyny

But if the wife payoff is highest on (not polygyny), lower on (polygyny, accept) and lowest on (Polygyny, reject) then the SPNE will be (polygyny, accept)

Anonymous said...


It seems that all people use game theory here. Do you think there is a pure strategy here?
I do not think so..

Why do assume that "I limited the study where the husband get highest payoff on (Polygyny, accept), lower on (not polygyny) and lowest on (polygyny, reject). The last one means monogyny with new wife after divorcing the old wife."?

Come one. Is it logical? Certainly the monogyny with new wife is better that monogyny with the old wife. The reason could be the "taste" and facts his new wife will be no/less problem with polygini (since she supposed tobe the second wife, however since the first wife reject the poligyny proposal, then she become the first wife)

For husband, it is better to have more wife that just 1. Thus, for husband, have more wife gives the highest pay offs. The second highest pay offs is get a new wive (means get polygini and then divorce the old wife). While the lower pay offs is monogyni.

The opposite situation happen to wive. The highest is monoginy, the second one is the divorced when polygini and the last one is the still marries while husband still poligyni.

Now, tell me, is there any dominant or dominated strategy? I do not think so. So, the only solution is you should use the mixed strategy.

berly said...

Hi Anonymous,

I limit the study to that particular case since it resulted with a interesting paradox of behaviour of one-can-only-keep what-she-willing-to-loose.

In my respond to comment to Ajo I wrote, "Otherwise the couple will stay together or there is nothing the wife can do to stop the second marriage (if the first wife refuse, the husband will divorce her anyway)"

In one shot game the dominant strategy will be husband marry the new wive (and divorce old wive if she reject).

But in repeated game, the prospectus wive will know that the polygyny-inlined-man is likely to get new wive(s) in the future and if her payoff is low for polygyny will seek monogyny inclined man for husband.

Anonymous said...

come one.

IN the first place, she already knew that she will be the second wove. The only thing that make it did not happpe is the facts that the first wive is already reject to be poligynied. Therefore, she already accepted to be polyginied.

If you use the repeated games, you should introduce the folk theorem. Or at least minimax and maximin for all the players. You also consider the discount factor. It is not as easy as you though and you write in this blogs, i guess.