| Strategic Modeling | |
|---|---|
| Details | |
| 12,000 ops | |
Effect |
Analyze strategy tournaments to generate Yomi |
Strategic Modeling is a project in Universal Paperclips.
Summary
By using tournaments you spend your ops (operations) to gain a varying amount of yomi, which are in turn used to purchase various improvements. Yomi are valuable in all 3 stages of the game.
This project is unlocked once you complete Donkey Space.
Mechanics
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The tournaments are based on many famous Game Theory related problems (such as "The Prisoner's dilemma", "Battle of the sexes", "Chicken", etc.) with the outcome rewards being generated randomly at the start of the tournament. While the "Random" strategy adds a little uncertainty, the general performance of each strategy can be predicted. The player can choose which strategy to back at any point before the tournament results are displayed.
The tournament cost is 1000 ops per strategy, and the number of rounds is the square of the number of strategies, so the potential "yomi" per "op" increases (because yomi earned is = to chosen strategy's score * number of strategies it beat). The length (duration, in real-time seconds) of a tournament depends on the number of rounds and so increases with the square of the number of strategies, plus a fixed delay of approximately 4 seconds when AutoTourney is enabled. it should be noted that if two strategies have identical scores, the simpler one will be ranked higher.
Each round is labelled as A versus B, with A and B being named as a temporary pair, a choice between two arbitrary outcomes, based on Game Theory problems, and some other cultural references. The name pairs have no effect on scoring, they are for informational purposes only.
Choice pairs are:
- cooperate / defect
- swerve / straight
- macro / micro
- fight / back down
- bet / fold
- raise price / lower price
- opera / football
- go / stay
- heads / tails
- particle / wave
- discrete / continuous
- peace / war
- search / evaluate
- lead / follow
- accept / reject
- accept / deny
- attack / decay
Regardless of the pair labels, each tournament is set up with a randomly generated set of reward pairs, the first element in each pair for the player, the second element for the adversary.
The game grid is generated as follows:
| Col. A | Col. B | |
| Row A: | a,a | b,c |
| Row B: | c,b | d,d |
Note that the values will always be identical in Row A/Col A (e.g. 9,9) and Row B/Col B (e.g., 2,2). Furthermore, the value pair will be reversed for Row A/Col B (e.g., 6,1) and Row B/Col A(e.g., 1,6). This equalizes the rewards for the player and the adversary when each choose the same strategy.
Consider the following example:
| Col. A | Col. B | |
| Row A: | 9,9 | 6,1 |
| Row B: | 1,6 | 2,2 |
Suppose Strategy A100 is selected ("Choose Row A 100% of the time"). The tournament runs all strategies against each other and sums the total rewards earned for each strategy pair (Random v. A100, Random v. B100, etc.). As said in Strategy A100, the rewards in this situation are likely (though not certain due to variable results from the Random strategy) to be greatest for this strategy and earn the most Yomi, in this case approximately 1500 Yomi.
Through the stages
Towards the end of the first game stage, the Theory of Mind project doubles the tournament costs and rewards.
At the beginning of the third game stage, the Strategic Attachment project gives the player yomi rewards for correctly predicting the tournament outcomes: a 50,000 yomi bonus is awarded if the selected strategy earns most yomi, with 30,000 and 20,000 yomi bonuses for the second and third place strategies.
The following table summarizes for each strategy the average expected result, average Yomi earned, and average Yomi with the above projects, based on a simulated run of 1 million tournaments. See the description of each individual strategy for the reward configurations where that strategy is likely to perform well.
| Strategy | Estimated Result | Estimated Yomi | Estimated Yomi with Theory of Mind | Estimated Yomi with
Theory of Mind & Strategic Attachment |
Win % |
|---|---|---|---|---|---|
| Beat Last | 1,083 | 5,516 | 11,032 | 39,102 | 27.56% |
| Greedy | 1,060 | 5,329 | 10,658 | 35,865 | 17.66% |
| Generous | 940 | 4,020 | 8,039 | 27,219 | 13.63% |
| A100 | 895 | 3,603 | 7,206 | 22,304 | 14.68% |
| B100 | 896 | 3,518 | 7,035 | 21,650 | 13.56% |
| Minimax | 853 | 2,884 | 5,769 | 19,105 | 7.40% |
| Tit For Tat | 899 | 2,742 | 5,483 | 12,744 | 5.29% |
| Random | 880 | 2,272 | 4,545 | 7,903 | 0.20% |
Trivia
- Strategic Modeling follows a concept in Game Theory known as a "normal-form game". A normal game is a type game that (typically) operates on a matrix, and follows a certain series of traits: each player acts simultaneously (or in ignorance) of the other player and all allowed strategies are detailed beforehand, as are all corresponding payoffs. More specifically, Strategic Modeling is an example of a game of "perfect information". From start to finish, all data is available to the players (you and the AI).
- Of the games mentioned in the summary, Strategic Modeling is most similar to "The Prisoners Dilemma", as the Prisoners Dilemma offers two simple choices, two players, and four predetermined outcomes based on the players choices.
- Interestingly, BEAT LAST follows a modified strategy as seen in Nicky Case's "Evolution Of Trust", in which it is determined that, in a game involving the choices "cooperate" and "cheat", a strategy known as Copycat will eventually succeed. This is because any time a strategy attempts to "cheat" it, it will cheat back, cutting its loses. Likewise, if a strategy "cooperates", then Copycat will make quite a bit. It can maximize its profits while minimizing its losses. However, this strategy doesn't quite work in Strategic Modeling, as evidenced by TIT FOR TAT's lack of success. Thus, BEAT LAST was created, a modified version of Copycat or TIT FOR TAT that aims to beat the last strat, rather than copy it, thus ensuring that if BEAT LAST lost the last round, it will likely win the next one.
- The chart in the article might be inaccurate, though I'm not really smart enough to challenge it. However, somebody on Reddit ran over 1 million games and compiled the average stats and percentages from that. You can find it here: https://www.reddit.com/r/pAIperclip/comments/7kh1t8/strategic_modelling_reexamined_in_full_tldr_beat/