When Can Limited Randomness Be Used in Repeated Games?

The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at generating random-like sequences, and true random bits may be unavailable. Even if the players have access to enough random bits for a single instance of the game their randomness might be insufficient if the game is played many times. In this work, we ask whether randomness is necessary for equilibria to exist in finitely repeated games. We show that for a large class of games containing arbitrary two-player zero-sum games, approximate Nash equilibria of the $n$-stage repeated version of the game exist if and only if both players have $\Omega(n)$ random bits. In contrast, we show that there exists a class of games for which no equilibrium exists in pure strategies, yet the $n$-stage repeated version of the game has an exact Nash equilibrium in which each player uses only a constant number of random bits. When the players are assumed to be computationally bounded, if cryptographic pseudorandom generators (or, equivalently, one-way functions) exist, then the players can base their strategies on "random-like" sequences derived from only a small number of truly random bits. We show that, in contrast, in repeated two-player zero-sum games, if pseudorandom generators \emph{do not} exist, then $\Omega(n)$ random bits remain necessary for equilibria to exist

Comparing knowledge sources for nominal anaphora resolution

We compare two ways of obtaining lexical knowledge for antecedent selection in other-anaphora and definite noun phrase coreference. Specifically, we compare an algorithm that relies on links encoded in the manually created lexical hierarchy WordNet and an algorithm that mines corpora by means of shallow lexico-semantic patterns. As corpora we use the British National Corpus (BNC), as well as the Web, which has not been previously used for this task. Our results show that (a) the knowledge encoded in WordNet is often insufficient, especially for anaphor-antecedent relations that exploit subjective or context-dependent knowledge; (b) for other-anaphora, the Web-based method outperforms the WordNet-based method; (c) for definite NP coreference, the Web-based method yields results comparable to those obtained using WordNet over the whole dataset and outperforms the WordNet-based method on subsets of the dataset; (d) in both case studies, the BNC-based method is worse than the other methods because of data sparseness. Thus, in our studies, the Web-based method alleviated the lexical knowledge gap often encountered in anaphora resolution, and handled examples with context-dependent relations between anaphor and antecedent. Because it is inexpensive and needs no hand-modelling of lexical knowledge, it is a promising knowledge source to integrate in anaphora resolution systems

Object-oriented Neural Programming (OONP) for Document Understanding

We propose Object-oriented Neural Programming (OONP), a framework for semantically parsing documents in specific domains. Basically, OONP reads a document and parses it into a predesigned object-oriented data structure (referred to as ontology in this paper) that reflects the domain-specific semantics of the document. An OONP parser models semantic parsing as a decision process: a neural net-based Reader sequentially goes through the document, and during the process it builds and updates an intermediate ontology to summarize its partial understanding of the text it covers. OONP supports a rich family of operations (both symbolic and differentiable) for composing the ontology, and a big variety of forms (both symbolic and differentiable) for representing the state and the document. An OONP parser can be trained with supervision of different forms and strength, including supervised learning (SL) , reinforcement learning (RL) and hybrid of the two. Our experiments on both synthetic and real-world document parsing tasks have shown that OONP can learn to handle fairly complicated ontology with training data of modest sizes.Comment: accepted by ACL 201

Dictionary matching in a stream

We consider the problem of dictionary matching in a stream. Given a set of strings, known as a dictionary, and a stream of characters arriving one at a time, the task is to report each time some string in our dictionary occurs in the stream. We present a randomised algorithm which takes O(log log(k + m)) time per arriving character and uses O(k log m) words of space, where k is the number of strings in the dictionary and m is the length of the longest string in the dictionary