Paradox of choice in social network games with product choice - - PowerPoint PPT Presentation

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Paradox of choice in social network games with product choice

Michael Raskin, raskin@{cs.au.dk,mccme.ru}

Aarhus University, Department of Computer Science

July 2016 (joint work with Nikita Nikitenkov, Moscow State University)

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 1 / 32

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Paradox of choice: Giving some players more options (or better payofgs) destroys the old equilibrium and the system switches to a new equilibrium which is worse for all players For example, a set of individual improvements appears that leads into a worse equilibrium It is easy to improve one player’s situation and make everyone else worse

• fg.

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 2 / 32

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Braess’s paradox

In a road network with travel time depending on congestion adding a new road can increase travel times for everyone.

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 3 / 32

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Braess’s paradox

In a road network with travel time depending on congestion adding a new road can increase travel times for everyone. Consider the travel times:

S T A B x+150 x+150 10x+1 10x+1

x is the number of cars (or thousands of cars) choosing this road Even split, time is 6x + 151.

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 4 / 32

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Braess’s paradox

Adding a road:

S T A B x+150 x+150 10x+1 10x+1 2x+1

For x ≈ 10 the switch to the empty shortcut with the cost ≈ 10x + 3(≈ 103 < 211 ≈ 6x + 151) becomes appealing

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 5 / 32

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Braess’s paradox S T A B x+150 x+150 10x+1 10x+1 2x+1

Everyone switches to the shortcut, time is now 22x + 3(≈ 223), but if one player switches back individually, time spent would be more than 10x + 151(≈ 251).

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 6 / 32

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Social network games with product choice 1 3 7 4 8 9 2 p1 p2 p3 p4 p5

Each vertex corresponds to a controlling player Each player has a set of available products with difgerent costs Available strategies are: pick a product, pay the cost, and get positive bonus equal to the sum of incoming edges from the players with the same product; or refuse to choose a product and get zero payofg (no cost and no bonus).

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 7 / 32

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Social network games with product choice

Introduced by K. Apt and S. Simon Existence of a Nash equilibrium is NP-complete [S. Simon] Related to the paradox of choice via individual improvements Individual improvement properties fjrst studied by K. Apt, S. Simon and

• E. Markakis

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 8 / 32

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Individual improvement chains

Individual improvement for a strategy profjle is a change of a single strategy that increases the payofg for the switching player Nash equilibrium means that no individual improvements are possible An individual improvement chain comes to a cycle or to an equilibrium (we assume that the player number is fjnite)

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 9 / 32

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Social network games with product choice: price changes

Raising the price of a product to a value larger than the sum of all the edge weights in the graph is the same as forbidding the use of such a product Similarly, allowing access to a product may be represented as lowering the price

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 10 / 32

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Social network games with product choice: individual improvement chains

A vulnerable game: allowing one more strategy to one player (or lowering the price of one product for one player) creates individual improvement chains and each of them leads to a strictly worse (for all players) equilibrium A fragile game: allowing one more strategy to one player creates individual improvement chains and each of them leads to a cycle An ineffjcient game: raising a price of one product for one player creates individual improvement chains and each of them leads to a better equilibrium An unsafe game: raising a price of one product for one player creates individual improvement chains and each of them leads to a cycle

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 11 / 32

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Social network games with product choice: individual improvement chains

Apt, Simon, Markakis provided examples of fragile, unsafe and ineffjcient games Also ofgered weaker notions of vulnerability (and provided examples) One of the weaker defjnitions: obligatory product selection, there is no refusal to use any product Existence of vulnerable games is proved in the presented work

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 12 / 32

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Cascade

Cascade is a black-box construction for building examples of social network games with product choice When the external conditions change, a cascade switches between two states by following the only possible individual improvement chain.

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 13 / 32

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Cascade

There are three products; product costs are lower than any of the edge weights Each player has at most two products available

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 14 / 32

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Cascade

There is one incoming control edge, depending on the incentives provided by this edge cascade is in one of two possible equilibrium states Changing the product choice at the origin of the incoming edge starts the

• nly possible chain of individual improvements leading to the other

equilibrium state One of the states provides much higher payofgs due to special weak links («emotional» links); these payofgs can also be applied to external players without afgecting their strategic choices

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 15 / 32

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Cascade — the two states

The good state: the incoming control edge incentivizes the choice of the product A, the outgoing control edge also incentivizes the choice of product A The bad state: the incoming control edge incentivizes anything else, the

• utgoing control edge incentivizes the choice of product B

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 16 / 32

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Cascade — the interface details

The product prices are low and equal. The cascade also uses medium-weight «inclination» links to ensure that there is a product that is better than refusing to choose the product. In the next few slides these inclinations are also provided to the players

• utside the cascade; in this case they are shown by emphasizing one

product in the list of options.

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 17 / 32

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A vulnerable game A 1

Cascade

BC 2 C

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 18 / 32

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A fragile game A 1

Cascade

BC 2 C

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 19 / 32

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An ineffjcient game

Cascade

BA 1 B

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 20 / 32

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An unsafe game BC 1 CA 2

Cascade

BC 3 C

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 21 / 32

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Edge changes

Instead of adding or removing products (or changing their prices) we can try to fjne-tune the payofgs by changing the weight of a single edge (low enough edge weights are equivalent to edge removal)

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 22 / 32

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Edge changes

The simplest example is universal reduction of payofg after an individual improvements chain started by reducing the weight of a single edge

Cascade

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 23 / 32

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Edge changes

You can either increase edge weight

• r

decrease edge weight and make the only individual improvement chain lead to: universally better equilibrium universally worse equilibrium individual improvement cycle

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 24 / 32

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Cascade structure

Three products Each player has at most two products available Product costs are very low but positive Three types of edges Two types of players: «humans» and «spirits», spirits have no free will Cascade is built out of three very similar ranks

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 25 / 32

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Cascade — the construction idea

The main idea is having three types of edges: Emotional edges: very low weight, very numerous, never afgect strategical choice Control edges: very high weight, often reward using products that are not available Inclination edges: high weight, but not as high as control edges, intended to reward using some product so that refusal strategy is not used

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 26 / 32

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Cascade — switching the state

For every player incoming emotional links switch between equal incentives for both available products and incentive for an unavailable product; the difgerence between incentives for two available products is never higher than one emotional link weight

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 27 / 32

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Cascade structure

Spirits A-stimulus B-stimulus C-stimulus A A B B C C

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 28 / 32

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Cascade structure

Ranks of humans A-rank AB A C A B A C ... A B A C

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 29 / 32

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Cascade structure

Cascade composition Spirits provide inclinations Main input controls a C-rank, which controls an A-rank, which controls a B-rank

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 30 / 32

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Possible next step

Is there a less rigid/more believable construction?

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 31 / 32

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Thanks for your attention! Questions?

Michael Raskin, raskin@{cs.au.dk,mccme.ru} (Aarhus University, Department of Computer Science) Paradox of choice in social network games with product choice July 2016 32 / 32