模倣子 Memetic Analysis of Faspeel Game

Faspeel Game - Memetic Index - Essay List 

THIS IS A WORK IN PROGRESS

Introduction

 I want to develop the matrix for the game. I'm working on the idea that memeplexes are networks. States allow deployment of memes, which lead to other states.

I've been listening to Linked again, and there are ideas like scale-free networks, hubs (1), average connection distance, network diameter, and so on. For one thing, networks with hubs are susceptible to attacks on the hubs. In other words, racism and other social ills could be dismantled by attacking the hubs of the memeplex network. These could be identified by examination of the memetic inventory of racism, but more scientifically, these hubs could be identified statistically, and then attacked using memetic engineering techniques.

Anyway, back to the game.

Game Set-Up

Okay, so what we have are the state of the positions of the coins, which are just "Away" and "Near" and this is symmetric for both players. The coins on the board are called the "showing" coins, or "the show".

fig. 1.1. "Near"

fig. 1.2. "Away" (starting set-up)

By the way, I'm going with only a coin on the board and a single coin covering the "secret" coin and that's it. The off-the-board coins are called "the message."  The message consists of a concealed coin, known as "the secret" and a coin covering it from view, called "the cover."

Okay, so every turn a player can make one of three moves, or memes:

1. "flip!" his "showing" coin

2. "tell!" by changing his message coins (2) 

3. Move his coin on the board (the "showing" coin)

3.1. Move "away!" if close to the other player's coin

3.2. Move "near!" if at the diagonal, to next to the other player's coin

3.3. "bump!" the other player's coin, if near, resulting in scoring (3)

Memetic States of the Game

There are some three orthogonal groups of states to the game, through which the system may vary independently, but which nonetheless determine which memes may be deployed, and these deployment opportunities are state-dependent. These consist of (4):

The state systems are the state of the showing coins on the board: "Away" and "Near"

The states of the message and showing coins of each player. The "other" player can have her coin on the board showing heads or tails as well as the "cover" coin. This gives us four possible states, "Other Show-Tails & Cover-Tails" or Ott, and then "show-tails & cover heads" or Oth, then Oht and Ohh. Similarly, the "self" player can have Stt, Sth, Sht, and Shh.

State Transitions

An example of a state of this system could include:

Away.Ohh.Sth

This could just as well be written Sth.Ohh.Away or even Ohh.Away.Sth. These state systems are orthogonal, so it's immaterial the order we write them, but there may be matters of convenience or clarity of notation at play.

Again, the memes of the system may be delineated completely. We'll add a couple for the scoring, which happens with a bump! meme, resulting in a both! score, or a bust! score (where players flip coins for the score). We're going to try to model the bump! meme as producing a "compelled" state (6) which proceeds automatically to either the both! or bust! meme and then to the Away state. 

away!  move away (when near)  Near.away! => Away 
near!  move close to the other player (when far away)  Away.near! => Near
bump!  try to score on the other player (when near)  Near.bump![both!, bust!] => Away

flip!  change one's showing coin

This can take the form of four different state transitions  

Stt.flip! => Sht  "flip showing coin from tails to heads with cover coin tails"
Sth.flip! => Shh   "flip show from tails to heads with cover heads"
Sht.flip! => Stt   "flip show from heads to tails with cover tails"
Shh.flip! => Sth    "flip show from heads to tails with cover heads"

or a shorthand for all cases could be: S[t,h]x.flip! => S[h,t]x

This means "flip show from tails or heads to heads or tails while keeping the cover the same." At this point it's unclear whether we'll use this notation in laying out all of the possible deployment descriptors.

tell!  change the message coins, the "cover" and the "secret" (4).

Stt.tell! => Stt    "show is tails, cover is tails, change nothing"
Sth.tell! => Sth   "show is tails, cover is heads, change nothing"
Stt.tell! =>  Sth   "show is tails, flip cover coin from tails to heads"
Sht.tell! => Shh  "show is heads, flip cover coin from tails to heads"
Sth.tell! =>  Stt   "show is tails, flip cover coin from heads to tails"
Shh.tell! => Sht  "show is heads, flip cover coin from heads to tails"

Again, a shorthand for this could be: Sx[x,t,h].tell! => Sx[x,h,t]

Then there is bump!, which only ever produces bust! or both! and takes the bumper to the Away state. It may only be deployed from the Near state. The both! and bust! deployments are So we have:

Near.bump!both! => Away  "the bumpee's secret is the same as the bumper's showing"
Near.bump!bust! => Away   "bumpee's secret differs from bumper's showing"

So really, with bump! it really doesn't matter whether both! or bust! happens, since you wind up on the Away state anyway. This is in keeping with the "compelled state" idea.

Deployment Descriptors

We should be able to list all of the transactions. It's states, and the memes which may be deployed, by whom, and which states those lead to. It's rather easy to be exhaustive with deployment descriptors, since one in principle knows all the states and memes beforehand and it's simply a matter of putting them all together.

The positional states of the showing coins do not impact the state of either the showing coins, or the message coins, so we shouldn't need to mention these.

Away.near! => Near

Near.away! => Away

Near.bump![both!, bust!]other.tell! => Away (7,8)

Then we have the two other operations which a player may undertake: flip! and tell! These only impact the state of the player's own coins, showing and cover.

This is interesting, and perhaps helps us to manage the complexity of the memeplex. There are collections of states, "state groups" might be a good term, that do not affect one another, and are only independently impacted by meme deployments. Meme deployments that cause state changes within a state group may be affected by other state groups, but do not directly affect those groups. For instance, a bump! changes the [Away, Near] state, and the result of the scoring depends upon the state of the coins, that is the Sxx and Oxx states, but does not influence them (7).

Network Description

I like to make matrix descriptions of the networks that make up memeplexes. A state transition diagram is a visual depiction of all of the possible transitions in a memetic system, but it starts to get unwieldy for large systems with lots of states and memetic transitions. The list of all deployment descriptors is probably the most sure-fire and complete description of a system, but it can be difficult to see how the system behaves at times.

Away.Sxx.Oxx.self.near! => Near.Sxx.Oxx

Near.Sxx.Oxx.self.away! => Away.Sxx.Oxx

Near.Sxx.Oxx.self.bump![self.both!, self.bust!]other.tell! => Away.Sxx.Ox[?]

[Away, Near].S[t,h]x.Oxx.self.flip! => [Away, Near].S[h,t]x.Oxx

[Away, Near].Sx[x,t,h].Oxx.self.tell! => [Away, Near].Sx[x,h,t].Oxx

The idea of a transition matrix set is a collection of matrices, each representing a "state" of the system, with agents along one axis and available memes along the other. At the cells of the matrix is future states to which the system transitions when said meme is deployed. In this game there are only two agents, and it's a turn-taking game, so we can perhaps dispense with the "agents" axis and use it to another purpose.

One way might be to skip this more rigid representation of states and memetic transition and just start with memes--since that's the more well-known quantity--and note all of the states that are connected to or from by any of these memes.

near!, away!, bump! link states Near and Away

   near! links Away to Near

   away! links Near to Away

   bump! links Near to Away

   ...then some stuff with bust!, both! and other.tell!

flip! links Shx and Stx, or Shh to Sth and Sht to Stt

tell! links: Sx[x,t,h[ to Sx[x,h,t]

    Shh to Sht

    Shh to Shh (no change)

    Sht to Shh

    Sht to Sht

    Sth to Stt

    Sth to Sth

    

    Sht 

Deployment Decision Processes

So one big goal is to devise an internal process, using the showing and message coins, to try to develop a model of the other's behavior, to try to guess whether they are trying to signal her intent.

Network Topology Implications

One thing to look for is whether this network has interesting properties, such as being scale-free or has hubs or what-have-you, or whether it's just too small.

Summary & Conclusions

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(1) As in memetic nexuses.

(2) Note that changing your message coins may involve actually changing nothing, or changing only one of the coins, the "cover" or the "secret", or both. It's possible to only telegraph having shuffled them to the other player, but not actually doing anything.

(3) When a player (the "bumper") decides to bump! the coin of the other player (the "bumpee"), we check the bumpee's "secret" coin against the bumper's showing coin. If they're the same, each player gets two points, if different, each player flips a coin. If both come up tails the bumpee gets three points, otherwise the bumper gets one point. Finally the bumper moves his showing coin to the "away" position and the bumpee repositions her "message" coins.

(5) I've not mentioned the "secret" coin of either player. Obviously the state of that coin is invisible to the other player. We'll try to get into how this can nonetheless be part of a player's decision modeling, both in terms of what she "knows" about own coin, and what she "thinks" about the other player's secret coin, based upon she can actually see, i.e., the show and the message, and the message he might be sending her with those coins.

(6) A compelled state is where a meme deployment puts an agent in a state where they have to choose between one or more memes to deploy. One way to denote this is with "immunomemetic notation," for example, bump!bust! => Away as opposed to something like bump! => ScoreState.bust! => Away

(7) Actually, the bump! meme changes the state from Near to Away, and it also changes the Ox[t,h] state, since the other player updates her message coins. Again, this is a compelled state.

(8) the full description of a memetic deployment is State.agent.meme! => NewState.  In most of this essay I've left out the agent, since it's implied to be the player. However, we could be specific by assigning the player whose turn it is as "self" and the other player as "other". Hence, Near.self.bump![self.both!, self.bust!]other.tell! => Away. Again we see how both! and bust! are memes in a compelled state, so in a sense they have no agent, as such, though it is still in a sense "self" the initiator.