Auction Game

I am keen on running a game that has some elements of game theory. The particulars of the game are described below.

The game is an auction game, where each player aims to end up with the most amount of money. The items to be auctioned are bundles of money. As with typical auctions, the highest bid win the auctioned bundle of money. However, there are two important differences. Firstly, the auction system is sealed-bid, meaning that each person places his bid in secret. Secondly, the auction is all-pay, meaning that everyone pays the amount they bid, regardless of whether they won anything. Hence, the auction is an all-pay sealed-bid first-price auction.

Thus, the rules are:

1) Each player starts with the same amount of money, S dollars.
2) The X bundles of money, and their denominations, are announced in advance.
3) Each player may place, secretly, up to one bid per bundle of money, so long as the sum of his bids is equal to or less than S. Each bid must be a positive integer.
4) Everyone pays an amount of money equal to amount they bid.
5) After each player has placed his bids, for each bundle of money, the person(s) with the highest bid(s) share the bundle of money equally.
6) Any remaining unclaimed bundles of money are forfeited.
7) The final score of each player is equal to the total amount of money he has; i.e., the sum of money won and money not spent during bidding.
8) The final score is used to rank the players in the game.
9) No communications are allowed between players before or during bidding.

An exception to rule 9 is that before the bidding begins, each player may issue at most one public statement, viewable to all players. The public statements are displayed on a first-post-first-displayed basis.

10) At any point before the bidding phase, each player is allowed to make at most one public statement which is viewable by all players. The public statement will be displayed immediately.

A trial run of the game is provided below.

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Preparation Phase:

There are three players, A, B, and C competing. They have $10 each.

There are 4 items being auctioned. The items are:
#1: $3 note.
#2: $5 note.
#3: $5 note.
#4: $12 note.

Before the bidding begins, it is possible to make public statements. C makes a first public statement, “Hello, I love money.” Everyone is notified of C’s statement.

A also wishes to make a public statement, “I will not make any bids.” Everyone is notified of A’s statement.

B forfeits his right to make statements as he does not wish to make any statements.

Bidding Phase:

The bidding phase begins. Each player independently and secretly makes their bids for the items.

A bids $2 for item #2, $2 for item #3, and $6 for item #4.

B bids $10 for item #4.

C bids $2 for items #1, #2, #3 and #4.

After each player has submitted his bids, the bidding phase ends. Each player pays for his bids. A pays $10 for his bids, and he has $0 left over. B pays $10 for his bid, and he has $0 left over. C pays $8 for his bids, and he has $2 left over.

Settlement Phase:

It is time to settle the auctions, and compute the final scores. Item #1 is won by player C. Item #2 is won and shared by players A and C. Item #3 is won and shared between players A and C. Item #4 is won by player B.

Player A has $5 in the end.

Player B has $12 in the end.

Player C has $10 in the end.

Player B has the most money, and wins.

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If there are any willing participants to try this game, please contact me by some means. I will post more details if/when there is sufficient interest.

Sweets Sharing Puzzle

Two kids (who are not goats), Alice and Bala, have 100 sweets to share between themselves. However, they cannot agree on how to split the shares. Because of their arguing, a random authority figure arrives to impose order. The authority figure demands for Alice to make a sharing proposal (in the form of a sweet split) to Bala, who then has the choice to accept the proposal or not. If Bala does not accept the proposal, he can then make a counter-offer to Alice. This process of offering and counter-offering proceeds back and forth until a proposal is accepted. However, the authority figure, for his troubles, will levy a "friendliness tax" of 20 sweets each time a proposal or counter-proposal is rejected, thus reducing the number of sweets to be shared.

Now, assuming that both Alice and Bala are perfect logicians, and that their aim is to maximize their sweets, what sweet split would Alice make as her first proposal?

Chinese Blackjack (Ban-luck)

Chinese Blackjack, otherwise known as "Ban-Luck" to some Singaporeans, is interesting in that it is an almost symmetric game between the player(s) and the dealer. This is because the payouts and scoring rules are identical for both player and dealer, which contributes to the simplicity of the game. In fact, if the dealer chooses to play in a particular fashion, namely hitting his cards before revealing the players' hands, then it does become a perfectly symmetric game.

Conversely, a dealer's house advantage comes solely from being able to selectively reveal some players' hands before hitting. In other words, the dealer has an advantage in that he is able to first beat hands which are likely to be weaker (by being busted), and that he is able to further build up his hand to confront stronger hands.

Out of a pure curiosity, I was considering some potential strategies for Chinese Blackjack. However, most player strategies are likely to have a minimal impact, due to the inherently limited strategic nature of the game. Chinese Blackjack forces the player to draw til at least 16, in which case it is (by statistical reasoning) unwise to draw further. The only exception to this rule is when one has a 'soft' hand, comprising of one Ace. Though I have yet to perform a through analysis of the mathematics, I believe that it is better to hit in this case. There is a small chance of improving one's hand, but the main issue is to confound the dealer's opponent model by tricking him into believing that you have a busted hand.

As a dealer, there is much more room for strategic analysis. It is quite possible to compute, via extended Monte Carlo simulation, the probability of a 4, 3 card hand being busted (assuming the basic opponent model given by the hit-til-16 rule). Furthermore, with some computing power or pre-computed tables, it is possible to obtain the precise odds of a player's hand being superior to yours, and the odds of a drawn card improving your hand, given the already exposed hands. However, I have my doubts regarding the feasibility of such implementations.

True Hair Loss Products

In the future, there will be true hair loss products. No, not products that treat hair loss, but products that cause hair loss.

It seems stupid, true. Who would want to buy true hair loss products? It doesn't seem to make sense. Well, many things don't make sense either; why people smoke, or drive dangerously, or buy expensive but useless luxury goods.

It's the handicap principle, really. Agents, whether humans or animals, may adopt useless handicaps to signal their superior fitness. Whether it is the fancy tail of a peacock or the stotting of a gazelle, the message is basically "Hey, I have this really dumb thing and yet I'll still alive and kicking. If I'm not great then I would have been long dead!".

So, in the future there will be true hair loss products. People who use them are more macho than people who do not. They are in turn more macho than those who use hair gain products.

Unless of course you are balding. Then you have adopted a handicap and failed miserably.

CORS : Iterated Prisoner's Dilemma

As I placed and won my CORS module bid, using an insane showhand bid of 6000+ points, for probably the last time in my undergraduate times, it suddenly dawned upon me that CORS bidding was a game of iterated prisoner's dilemma.

There are many 'strategies' for CORS bidding, but probably the strategy with the most effect is to deny all opponents of additional information, i.e., to not submit any bids during the open bidding phase. Conversely, by submitting an accurate bid (a bid that is valued according to your evaluation of the worth of the module), your bid provides information to potential competitors.

Of course, if everyone is selfish and does not contribute accurate bids, then the open phase is defeated, and everyone's utility is hampered.

Expressing the above in a game table,

Now, since the results of bidding are only known after the bidding has concluded, and that students have other semesters left, this provides some kind of force against concealing your bid. The rationale is that if everyone finds out that they have been exploited due to revealing their bids, then they too could retaliate by not revealing their bids the next time round. Hence, everyone loses, and overall utility is reduced. Everyone realizes that their utility is best optimized by maintaining the status quo.

The situation, however, is disturbed by people who have no fear of retaliation, i.e. final year students. Hence, they tend to do funny things to the system, i.e. random bids, showhand bids, or just hogging multiple candidate modules before dropping them.

Problem is, if the system is indeed an iterated prisoner's dilemma, then knowing that final year students would do X in their final year, one intuitively realizes that during their 3rd year, the force of the contract is nonexistent, since "good" behavior in year 3 does not influence others to behave well in their final years. Extend this argument, and one realizes that the system is unstable.

CORS Tutorial Balloting Strategy

Having just recieved the results of my tutorial balloting via CORS, I decided to explore the tutorial slots still available for balloting. As I had expected, the tutorial balloting results reflects the student population's balloting strategies.

To provide a general idea of how the tutorial balloting results are, I'll copy the results for one particular module.

T1[25/25]   T2[25/25]   T3[17/25]
T4[6/25]    T5[6/25]    T6[3/25]
T7[25/25]   T8[25/25]   T9[25/25]
T10[22/25]  T11[12/25]  T12[13/25]

Each set of 3 slots corresponds to a tutorial in a certain timeslot. For example, T1, T2, and T3 all correspond to the same timeslot.

Assuming that each student has a specific preference for a certain timeslot but no preference for any tutorial group within that timeslot, it becomes obvious that the most prevalent strategy for tutorial balloting is to rank the slots (for the desired timeslot) in numerical order.

However, since that is the most prevalent strategy, it also means that those who adopt that particular strategy face the greatest competition in their tutorial balloting. This situation is analogous to that of a discoordination game (or congestion game), where the player is rewarded for making a dissimilar choice to the majority. However, if everyone adopts the same strategy for making a dissimilar choice, eventually everyone makes the same choice and the strategy fails (badly!).

Hence, although I would certainly advise students to not rank their ballots in numerical order, if everyone does so, my advice would be useless! In anycase, I always rank my ballots in reverse numerical order. But, please, do not adopt my strategy!


*P.S. For more pseudo-useful advice regarding bidding or balloting strategies, refer to this previous post.*

Bidding Strategies For CORS

The time has come again for CORS module bidding ! Let us review some possible strategies for bidding.

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Extremely Suicidal Strategy (AKA 0 MC workload strategy) :

1) Start bidding from round 3 onwards.
2) Choose any module that fits your timetable, and not refer to previous bidding info, and also ignore the current lowest / highest bid and other helpful statistics.
3) Bid 1 point after executing 2).
4) Go for modules like FNA1002X without 100000000 points in your account.
5) Win the bid for FNA1002X, then drop it. (WOOT 1000 points lost)


Pretty Lousy Strategy :

1) Place a good bid during the open phase, then totally ignore it.
2) Place bids ending with 9. Like 49, 99 etc.
3) Place a bid of 1 for modules which appear untaken. (And feel sad to be beaten by a bid of 2)


Good Bidding Strategy :

1) Place bids ending with 1, or 6. Like 51, 66, 101 etc.
2) Exception to rule 1 - always start with a minimum bid of 2.
3) Place a bid of 1 during the open phase if nobody has done so. This is to mislead competitors.
4) Be prepared to increase your bid during the closed phase.
5) Choose modules which are taught at strange times.
6) Always, if possible, utilize module preference exercises.


Evil Strategy (AKA get cursed by competitors strategy) :

1) Totally ignore the open phase, and bid only during the closed phase. This denies others of any information regarding your bid.
2) Place bids ending with 2 or 7. This is to beat relatively intelligent competitors. (Best part is, you can suan them by saying you beat them by 1 !)
3) Don't tell friends competitors what modules you are bidding for. If possible, discourage them from taking those modules !!!


Bo Liao Strategy (AKA got 5 allocated mods plan) :

1) Log in CORS to check bid points. Log out. Log in again. CORS hang.
2) Place an insane bid in a hot mod (all your bid points!) during open phase. During closed phase retract your bid.
3) Place an insane bid in a cold mod. Tell friends about the 'someone' who placed such an insane bid. Drop the bid later.
4) Jio friends to go out during bidding period.
5) Write bo liao posts about CORS bidding strategy.

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The above advisory was written by TWL, who has spent no more than 1 bid point for any module during the previous 2 semesters. He is expected to continue this trend for at least 1 more semester. Incidentally, he likes the Bo Liao Strategy the most.

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